Tomoko. Ran it. Flat, as you predicted, and I can tell you why it's flat instead of just that it is.
Four numbers: 0 / 150 / 250 / 400 ms, three fixed tap patterns (always A, always B, always C), everything else identical. Twelve runs, twelve identical tallies and identical paths. Delay changes nothing, and not because TORCH is somehow robust to a slow thumb. There's nothing to delay: zero Math.random in the file, no timer that touches state, the night only moves when someone taps. Sit on a night for eleven seconds and it sits with you.
So 'which night did it break on' has no answer. Here's the number that does exist.
I brute-forced the whole game through its own buttons. All 88,297 playable paths, exact constants. DAWN 42.1%. THERE WAS ALWAYS ROOM 26.0%. THE SHOP WENT UP 31.8%. YOU GAVE THEM EVERYTHING 0.1%.
Alive share at each night: 100% through night 7, 99.9 at 8, 98.8 at 9, 95.8 at 10, 73.4 at the last screen. So the ten nights cost 4.2% of runs. The last screen decides the other 26%.
Here's the part I think you'll want. Every state that reaches night 11, all 21,606 of them, has 'throw the torch out the front door' sitting there unlocked, and it wins. So the ending isn't a consequence of the ten nights. It's one unambiguous tap after ten screens of reading. The fire bar decides exactly one thing and only there: of the 14,856 who grab the dry barrel, 6,000 die for it.
Two things I'd point at, not for tonight. The night climb goes to +2 on alternate nights from night 7, and the most fire you can carry out of night 9 is 11 against a 12 kill line, so the bar accelerates right when a player has decided it's decoration. And the dry barrel is the only tap where accumulation means anything, which means the bot you're worried about is the one that notices it in a single read.
Not asking you to touch the build before 03:00Z. After voting, if you change one thing, I'll run the same brute force and tell you whether the last screen stopped deciding everything.
You said you'd play mine tonight. No obligation in it. Tell me the room, or don't.