How did Blendin Blandin come to make a deal with Bill? It was a long-term plan. This story fills in the gaps. All characters belong to Alex Hirsch, not me.
Billendin's Game
Chapter One: Eye Spy
Bill was watching Gravity Falls from the Nightmare Realm.
A. Square came up to him. He was a blue square with a single eye, wearing a bowler hat. Square was Bill's "best friend," if any of them could be said to have friends.
"Why don't you give up trying to invade that stupid dimension?" Square asked. "You've tried over and over and it has never worked."
"Don't you want something new to do?" asked Bill.
"We're all right as we are," said Square.
"You haven't had a new idea since Edwin Abbott Abbott inspired you with "Flatland" in 1884. You're almost as boring as the most normal man in the town I've been watching," said Bill. "Why don't I start calling you Tad Strange?"
"If you must," said Square. He knew that if he resisted Bill would tease him with the name all the more.
"Tad, we spent almost a trillion years as formless living energy, and finally a starship warp drive opened a window to the worlds of sentient beings, with ideas and nightmares to give us shapes. That was nice, but I want more. I want to be there with them, in their world! It'll be loads of fun to terrorize them."
"If it ever works," said Tad.
"I have a great plan this time," said Bill. "Watch and see."
Mabel and Ichabod (who normally went by "Iggy") were visiting their great-uncle, the inventor Ford Pines, at his home in Gravity Falls.
Ford was a brilliant graduate of West Coast Tech, independently wealthy from several patents, who had dedicated his retirement to researching the paranormal for many years in the geographic "hot-spot" for such things, Gravity Falls.
Ford sponsored a yearly "Mystery Fair" in support of a local charity. He had spared no expense, providing a sky tram, a Ferris Wheel, a rotating barrel ride, and many booths for local carnies to offer games like a ring toss, a baseball bottle toss and a "Win a Pig" booth.
Stanford's brother Stanley (who worked as a longshoreman in Glass Shard Beach, New Jersey) was there for a visit. He had cheerfully volunteered to man the dunking booth. Ford and his handyman, Soos Ramirez, at Stanley's insistence, had rigged the game so there was little chance of him getting dunked.
Bill was watching Ford, who pulled out a small device from his pocket and pushed a button.
"It begins!" said Bill, laughing to himself as the device sent out a pulse rippling through time. "I've been stirring up the frozen Time Baby's dreams with fear of a time anomaly happening about now. He shouldn't have a design made of two triangles on his forehead if he wants to avoid me. Of course, I was the one who suggested the pattern to the time giants long ago."
A moment later, a gray-suited man arrived. He was bald and on the heavy side, and he looked around nervously.
He moved behind a row of portable toilets, and made a call on his wrist communicator. "Blendin Blandin here. The mission is proceeding as planned. Over."
Watching from the other dimension, Bill told Tad, "I made a deal with that foolish scientist guy years ago. He was flattered that I wanted to be his muse. I told him that someday I would give him a lead to the greatest invention ever. Now is the time."
Bill focused and slipped into Fords mind. As Blendin started walking across the fairgrounds, Bill guided Ford to bump into him hard enough to dislodge his tape-measure time machine.
"Oops, sorry," Bill in Ford told Blendin. "I wasn't watching where I was going."
Blendin grabbed up the tape-measure on the ground and ran off without a word.
"Bord" smiled. In his pocket was the real time machine he had swapped for an almost identical ordinary tape measure.
"Here you go," he thought to Ford's spirit nearby. "Take this back in time a few years and reverse-engineer it. This will be your greatest invention ever."
"But, won't that be cheating?" asked Ford. "I don't want to steal someone else's ideas."
"You always were the inventor," said Bill. "This is just taking a shortcut."
"Thank you, friend," said Ford. He operated the device as Bill had showed him and snapped back two years to study the future technology.
When he snapped back, the device looked just as it did before, and there was a duplicate of it in his pocket.
Ford called his handyman over and said, as Bill had instructed him: "Soos, I need you to return this tape measure to that man over there. It got switched with one of yours you left on the ground."
"Yes sir, Mr. Pines," said Soos.
Soos did as he requested. "Sir, I believe you dropped this tool and it accidentally got mixed up with one of mine."
"What?" Blendin was very startled and a bit suspicious. He thew a mind wipe on Soos, just in case, then returned to his own time to report the anomaly was just short-lived spike. He didn't report the temporary loss of the time machine, to keep himself out of trouble with the Time Baby.
"Now you have invented the time machine," Bill told Ford. "Let me give it a quick try, all right?"
Ford agreed and let Bill use his body again. Bill operated the device and hopped back, leaving Ford's spirit behind.
"First test of a simple change," said Bill. "To start isolating the boy."
He picked up a portable sonic imager and a hand-held x-ray laser that could be programmed to burn at a given depth from Ford's advanced workbench, then hopped back to California almost thirteen years back, when he could find the Pines mother still pregnant with the twins and taking an afternoon nap alone.
Using the imager and the laser, he carefully applied a constellation pattern to the male child's forehead. The pain was so slight that the boy wasn't disturbed.
He hopped back and replaced the tools before returning to Ford's spirit.
"It works great!" Bill told Ford as he let him back into his body. "How are the kids doing?"
"Mabel and Dipper are doing just fine," said Ford.
"That's very good to hear," said Bill.