The next morning (by the Time Delia consented to leave it was late into the evening and Mr. Fuji insisted they stay the night.) Mark and Delia said their goodbyes and departed.

They hadn't gotten far before Mark revealed there was something on his mind "Delia, there's something I want to tell you"

"What is it?"

"Delilah, I care about you. do you think that…" he trailed off but Delia knew what he meant.

"This is a bit sudden don't you think?"

Mark's face fell "does that mean-"

"Not at all. I would love to spend more time with you. I mean, if you're sure."

"That's great to hear" Mark said obviously relieved. turning serious he added, "Team rocket may still be after me though so we should find somewhere to lay low for a little while longer."

"A friend of my mother lives at the lighthouse at the edge of a cape north of cerulean city. She was one of the kimono girls from Johto but recently moved to Kanto and had a son. It's not too far from here, though we'll have to head through the infamously treacherous rock tunnel. I think I could show you the way, but first… you'll have to catch me!" Delia took off running, all the while laughing giddily.

You would probably be quite surprised how much research into Japanese courtship I did to ensure this concept fit my view on it (that the concept as a whole is most certainly Japanese let's be honest as a story for ten year olds 20 years ago this wouldn't be acceptable outside of Japan.) basically there are four stages:
Social gatherings; this is usually where you would meet your dates for the first time (due to the circumstances I skipped this phase)
Dating; just getting to know each other. At this time they aren't considered "in a relationship"
Confession of love; THIS is what marks serous dating this is also the part
I just highlighted of course just like here women can make the confession it is even more strongly expected of the male. Female confessions are near taboo status but are becoming more common.
Finally the proposal; once again it's STRONGLY expected of the male but not required.