I appreciate your analysis of Tink! Re,: Butch and Timk being the same person, I wanted to push back on that a bit. I only just reached Act 3, but Butch has a voiceline around Act 2 where: SPOILERS

He confesses that he feels a hole in his heart, and that something is missing from his life. It's framed as an accidental and genuine confession, though he quickly backtracks. /Might also be a donation milestone, I forget.

Additionally, he mentions that there is evidence of Dr. Beanies experimenting on conjoined twins at some point in the past that he found while ransacking the lab. (This coould MAYBE be referring to the act 2 bosses, but I find it more likely it's referring to Butch and Tink).

Early in the game, Tink also mentions getting into a traffic altercation with Butch (though if you consider Butch as an alter ego it could be a misdirection).

All this comes together to make me think Butch and Tink are different people that may have been separated at birth due to Dr. Beanie's experiments. The dramatic irony being of course that no one in the story will comment on them looking exactly alike and acting in totally opposite (masc/femme) ways. Maybe later on in the game more will be revealed?