Route 16: West of Celadon City, this path does not lead to Saffron City at all. It's a fairly short route, and Hogoki's going down it fairly slowly and leisurely while going the wrong way sometimes with Foccai's help.

As he nears the end, however, he encounters a station, and behind it is something he normally only sees in cities: A paved road. Of course, that piques his curiosity, and he heads inside while looking around – it's just a tunnel with a gate and a desk and two guards- Oh.
"Hey, kid. You got a bicycle?" Strange question to ask.

"I've been on one before, but I don't have one on me-"
"Then what are you heading towards Cycling Road for? You've got nothing to ride with!"

"Even if I don't, I've gotta go through it to keep traveling, right?" Foccai looks like he's questioning his life choices right now as he gets recalled- Wait, why did Hogoki recall him?
"You're not getting past us, kid, it's for your own- Holy shit don't just dive at us that fast-"
"He's fucking going in, go get-"

"Nah, he'll be run over by a motorcycle or something before we get him."
"...You've got a point there." They both sighed in defeat before having another sip from their drinks.

Meanwhile on Cycling Road, Hogoki is cheerfully jogging the route after having basically jumpscared the guards into letting him through. Foccai's still in the ball, no sane person would let Kwaru out right now, and Hanako… well, he'd probably send her to that daycare guy so she wouldn't be attacked again next time he saw hi-
...Well, that was a close call with that one bike-
Why was there a motorcycle right behind him?! He barely dodged it!

...That one bike that just passed by looked oddly car-shaped, and… wait, was that a preschooler on a tricycle just now?
"How are you able to ride here?!"
"Me has bike now!"
Okay, that's it, he had seen everything surely. He was going to just keep walking, he could see the end of the road a little far off...

And he just heard a cracking sound from his backpack followed by what sounded like a quiet beeping… Which the incubator and its egg happened to be inside his backpack… Oh no.

Yep, time for him to run down Cycling Road, so what if he was speeding? It was the cyclists' problem if they couldn't go faster and keep up with him, and this was an emergency, he needed to go fast! Just keep running, yeah, just keep running as fast as possible, he was almost there, just needed to dodge that crack in the pavement-

...Ow. Guess he didn't have working brakes. At least he was out of the way of bikes now, though… Now he needed to check the egg, so he took out the incubator from his backpack, and to his surprise, it wasn't just a bunch of shell fragments and yolk, nope. Instead, the egg was cracking increasingly more while moving from the inside, and soon whatever was inside managed to properly break the egg open, causing the incubator to also open and reveal… a baby Eevee!

So said Eevee was just staring at him until it started crying, and let's just say baby Pokémon shouldn't be able to cry that powerfully that Kwaru immediately exited his ball and was about to challenge it before he realized what was making that sound and scratched his beak with his wing. Meanwhile, Hogoki got a little frantic again as he tried to find ways to do… well, anything, how would he know what to do here?! He never had training in baby Pokémon! Thus, he just looked for ways to find info, namely on the map, the thing Oak gave him and he couldn't remember the name of at the moment, his backpack, Foccai (who just shrugged in defeat), and even the new badge case he'd managed to buy, until he checked the incubator again.
"'Call this number for help with newly-hatched Pokémon'… They couldn't have said it sooner?" He couldn't have looked sooner? That said, he dialed the number almost as soon as he could see it, and a familiar voice proceeded to answer.
"Brock of the Pokémon Breeders' Association speaking, how can I help ya?"
"...You help with this stuff?"
"Yep, it's a life goal- Hold on a minute, I know that accent! You're that kid I sat down with some months back, how are ya?" ...Uh, did he forget his job?
"I was doing great, but right now I've gotta take care of an Eevee that just hatched!"

"Right, my bad. So start with cleaning up any egg fragments and all that-"
"Kwaru, use a really weak Water Gu-"
"Wait, try a rag firs-" Water sounds. "...Can't blame ya, but hope the incubator works still."
"It looks like it works… kinda?"
"Do the parts still move? That's all you need."
"...Yep, they do. What about the Eevee?"
"Well, you start by feeding baby Pokémon berries if you've got any…"
"...Kwaru's feeding her bread, though."
"Ah, whatever, it won't poison her, just find some berries later. Now you catch her when she stops crying, should be soon. Don't throw the ball, just tap the button on her head." Well, he just learned how to catch a Pokémon, it seems. "Once you let her out, wait until she gets interested in Pokémon battling and then train her from scratch. From there, she'll be like any other Pokémon! By the way, how's that kid I had you help out in Mount Moon? She was all shaken up when she returned my Geodude in Cerulean."
That was a long pause. "...Probably just nerves when she realized she was a trainer." Nerves after a realization related to training, alright.

"...Yeah, I can see that. Anyway, you've got all you need to raise that Eevee, but if you need more help, give us a call! Gonna hang up now."

As the call ended, Hogoki noticed a decent amount of people were around and that Eevee had stopped crying while looking at all of them… so he took a ball off his belt to lightly tap the back of her head. The newborn Pokémon proceeded to enter the ball, and there weren't even any shakes before she was caught, probably because she had no idea what was happening. And then upon being sent out again, Eevee just… uh, looked very confused before walking around and then having to be picked up as like ten people proceeded to surround Hogoki and his team at once.
"Hey, kid, take a moment to battle!"
"We're raring to go today and you're up!"
"Start with the duck, looks strong-" Water Gun to the face, appropriate reply. "...Or the seal thing, maybe."
"Even if you use the Eevee, we'll take you on, so don't be a coward!"
"W-Whoa, wait a second, I'm busy taking care of-"
"You just left Cycling Road, kid, we're giving you a challenge after that leisure trip!" …Leisure? Running down Cycling Road?
"I'll fight ya when I get the chance, right now we've gotta go!"
...Hogoki can still run after reaching top speed on a paved road? Good thing his Pokémon can follow him at this speed.
-

"...So, Misty, the kid's alright. He called me earlier, acted like a normal kid, didn't seem like he was in a rush to fight with baby Pokémon before they could start or anything like that. ...Yeah, crazy, ain't it? He's practically unrecognizable if you're looking for a Taki household member- Wait, what was that just now? ...Damn. That's gotta be hard on him. Maybe Erika can sort something out if he stops traveling. Anyway, all my siblings are fighting again, I've gotta sort that out, have a good day- Ow, what's with the frying pan?!"
-

He finally escaped the trainers… he finally found some berry trees… he finally managed to stop Kwaru from eating half of them… Being a trainer with a new Pokémon wasn't easy. Still, being able to relax under some trees with his Pokémon was worth it. Foccai was practicing some acrobatic skills, Kwaru was trying to sleep upside down, Eevee was eating berries like he ate rice, and Hanako… Wait, he hadn't let Hanako out since he ended up having to catch her last night, had he?

Well, that certainly had to change now. He took the ball off his belt, pressed the button, apparently didn't press it hard enough so he did it again, then looked at the ball very confused. ...Why wasn't she coming out? That wasn't what he'd expect at all… Maybe she just wanted to rest more. He couldn't blame her, so he'd let her stay in a little longer…

Foccai was helping Eevee practice some basic battling moves, so Hogoki supposed his own work was done here for now, and he was still tired from yesterday… so he accidentally fell asleep until a couple hours after midnight.
Onward to Saffron? Or wherever they're going once he wakes up...

...

...

...

"Alright, everyone! We're setting off, let's find a town before the sun rises!"

It was two in the morning on Route 18 when Hogoki woke up. He'd given Eevee some more berries because she had been training hard since he fell asleep and seemed to have even fought a few wild Pokémon at some point, but immediately after that… he'd said the above, and all of his Pokémon responded as if they hadn't expected that. Foccai accepted his fate shortly after and Eevee was eager to go, but Kwaru… uh, tried to sleep more on the ground. As a result, Hogoki tried to pick up the duck, and he flailed so much that any potential rest ended up being useless by the time he decided it wasn't worth fighting anymore.

And on that note, we follow this boy and his team as they go forth into the Kantonian night. Foccai has the map and Hogoki, Kwaru's eating the grass, and Eevee's… being Eevee again and fighting every wild Pokémon she can encounter. Slows them down, but it's worth it, yet there's a problem: Eevee can't fight well enough to defeat wild Pokémon by herself yet, so Foccai or Kwaru has to step in either before or after she gets knocked out by her opponent in order to defeat said opponent. There is the occasional win, but it's like one out of every five fights… We don't even talk about the trainer battle attempts.

So of course, after yet another failure to fight a Rattata, Hogoki decides to step in. "You have a lot of trouble dodging, don't ya?" That was a frustrated nod, if a tired one. "Well... I'm your trainer, so how about I help ya? I can tell you how to dodge, when to attack, how to attack…" ...It took a second for the fluffy brown whatever-this-is to give a response, but that seemed to be confused acceptance. Suppose she was still wild to an extent. "Alright, then we can start with that Doduo!"

It took a little while for trainer and Pokémon to get in sync, but eventually, they were able to fight as a pair, and when that happened… well, they started racking up wins little by little, and eventually they were winning every other battle against wild Pokémon, and the occasional trainer battle, and sometimes Eevee even won a battle against a wild Pokémon by herself without much difficulty.

You know where the best battles in Kanto are found, though? Cities. And they've finally arrived…

"...Fuchsia City? We were heading for Saffron, though, right?"

...exactly where they were going to end up in when Hogoki set the initial course in Celadon. Foccai definitely wasn't amused, Kwaru facewinged, and Eevee was surprised but not too bothered, mainly because she tried to challenge a local trainer who was heading to the Pokémon Center.

"Ah, whatever, we can just go straight to the gym! ...Once we figure out where it is." Kwaru started some exasperated quacking to himself right about then. And with that, they headed for the Fuchsia Gym, getting sidetracked constantly by either a battle or Hogoki's poor sense of direction.

When they arrived, it seemed surprisingly simple: Go down the very obvious, if strangely long, path directly to the battlefield. And then the invisible walls made themselves painfully obvious.

"Ow! Why's there gotta be so many of these...?"

"It's a maze, kid... Gym leader's at the end, good luck."

So basically, one hour later, he was halfway there. Three hours in, he was two thirds of the way there, but Foccai was having trouble navigating right, so... uh, there were problems now. It took five hours in total for Hogoki to get out of the maze, and by the end, he was having to lean onto the invisible walls for a few seconds to progress while having Kwaru make sure he wasn't walking backwards. But he was now at the battlefield, and the gym leader... looked very tired, to say the least.

"...You want to challenge me today, child?"

"I'd almost say no after the maze, but I don't wanna go through that again..."

"Quite a lack of fighting spirit, I must say... That said, how many badges have you earned?"

"Four-"

"Then I, Koga, shall show you that my badge is not earned with such ease... Because you must now face my entire set of Pokemon at once."

"W-Wait, why's that?"

"My trial requires true adversity to be overcome in order to earn my respect, and I am in no mood to take pity on another trainer! Now, let us begin."

So that's how Hogoki found himself face-to-face with two Venomoth, a Muk, and a Weezing. They didn't seem especially happy either, and everyone being tired probably didn't help matters, so he took the obvious choice. "...Foccai, start with Bubble on the Weezing- Wait, Kwaru, what're you-"

It all happened very suddenly. Before Foccai had the chance to attack, Kwaru had suddenly flown up high and started to screech angrily with increasing loudness as he began flapping his wings faster and faster. At first, it was a slightly more powerful Gust, but then it transformed into something nobody had expected to see today.

Hurricane: A move where the user creates increasingly strong winds that, if not prepared for, can defeat many opponents at once in a large, localized windstorm. And it was defeating opponents right now, alright, but it was also destroying the gym and giving Hogoki and Koga quite a lot of trouble standing even after Foccai was recalled. Hogoki even had to hold onto an invisible wall that was shaking from the sheer power of these winds.

And then, as if it wasn't strong enough, the end of Hurricane involved the winds rapidly petering out in the form of an explosive burst in all directions. That knocked Koga off-balance, and Hogoki and multiple invisible walls just fell such that there was now a clear path from entrance to battlefield... and finally, the chaos ended, with everything scattered about, Pokemon knocked out, and a Ducklett landing on the ground to laugh at his dizzy trainer's unpreparedness.

Said trainer was seeing about three Ducklett right now, but he was staring at all of them in shock from how Kwaru managed this. His vision quickly refocused at the sight of Koga no longer having his jaw dropped in a similar shock at the ceiling being damaged and walking towards Hogoki with a face of disdain.

"...Now, perhaps you did not intend to cause such destruction. Or perhaps this was your strategy. But even as I hand you my Soul Badge, I must say that perhaps you've spent far too much time in this building for your own good already."

...Yeah, when someone says that, you leave their territory, no questions asked. In this case, you take the badge and recall your duck, nod, and leave immediately. And since he was a Gym Leader, the whole city was Koga's territory...

Onward to wherever he was supposed to go!

...Or at least, outside of Fuchsia. They were too tired to go further than that right now, so once they managed to escape Koga's domain, they decided to have a nice long rest.

Foccai was just trying his best to rest, Kwaru was eating all the berries again, Eevee was already trying to fight something again... or play, who knows at this point?

The strange part was that Hanako still hadn't left her ball. At this point, Hogoki didn't want to wait any longer to try again, and if he failed, well, he'd just have to get to a Pokemon Center soon. So he took the ball off his belt, pressed the button to send her out, and she actually materialized this time...

Problem is, after the initial disorientation, she ended up frantically hurrying in a random direction with a face that conveyed more panic than words ever could. So of course that meant everyone had to follow her, difficult as it was to do so, though Kwaru could keep up because flight tends to be faster than legs.

When they finally caught up with her, she was a tearful mess in a bush, quills extended and fear still in her eyes. So it was clearly time to comfort.

Hogoki started out by being himself. "Hey, hey, it's been a few days since we left Celadon... Haven't seen any fire types around, though I guess I could catch one when I do- Ow, Kwaru, why'd you slap me for?" Exasperated quacking and a sigh from Foccai.

Speaking of Foccai, he tried to do the same to comfort Hanako, but around a third of the way through she started staring at him like he was talking nonsense before he got Razor Leafed into stopping whatever he was on about. Like Pokemon, like trainer, suppose. It did manage to calm her down somewhat, though she was still quite nervous... and Eevee managed to jumpscare her by accident.

...Well, they'd been a while resting and running, so suppose they had enough energy to set off again, because Hogoki and Foccai immediately consulted a map.

"So which way did we go?" Bwark. "East? ...Which way is that?" Bwark. "Oh, right... Then how do we get to Saffron?" Took a second, but Foccai pointed to Lavender Town then slid his flipper left. "...We go back to Celadon and then go south, then?" Collective faceplant from the Pokemon right there. Even Kwaru started telling him the right way. "Northeast then west? ...Think I know which way to go now!" HE DEFINITELY DIDN'T WHY IS HE RUNNING NORTH, EVEN THE POKEMON ARE PUSHING HIM THE RIGHT WAY NOW

ONWARD TO LAVENDER TOWN