What *exactly* is the action / event that fixes your choice of Grimm Troupe quest?

I recently found out that there are 2 options of the final portion of the Grimm Troupe content.

• Fight the Nightmare King

• Help Brumm banish the Troupe.

My wife and I have 2 saves, we've both beaten the Troupe Master once.

• I have already collected the final set of Grimm Flames, and attempted the NK fight a few times.
• My wife hasn't collected any of those final set of flames, though.

But when either of us

go back to the brazier in the Howling Cliffs, we don't find Brumm :(

I'm less surprised that I can't. But I expected my wife's game to still allow that path?

Exactly what determines which path you're on, and is it possible to change it at all? (e.g. by editting the save file? I know there are programs that can analyse a save file and tell you what you should look at next, if you're "stuck")

Just verified using save states:

The exact action that forces you down one road or the other is either killing Nightmare King Grimm (getting defeated in combat and returning to bench doesn't count), or delivering the final blow to the torch in Howling Cliffs (initiating the process, having Brumm damage the torch, and hitting it some yourself doesn't matter).

That means literally you can change your mind up to the very last moment before given ending.

Talking to Brumm in one of small houses in the Distant Village (while having Grimmchild equipped) is necessary to 'unlock' the alternate ending - you won't meet anyone at the torch if you don't talk to Brumm in Distant Village houses, and it's possible after defeating Troupe Master Grimm (accessing the third set of grimmkin) - before that Brumm is in Dirtmouth and talking with him only gives lore. Killing three Nightmare Grimmkin unlocks the 'main' ending, but you can talk to Brumm at any time between finishing the two Grimm fights and delay the decision until the very last moment.

In fact you can lose the fight to Nightmare King Grimm, decide it's too hard for you, find Brumm in the Distant Village and then go destroy the torch. Or you can visit Brumm right after the first Grimm fight, damage the torch (but not destroy it), then kill three Nightmare Grimmkins and Nightmare King Grimm.

In your case, I just suspect neither of you talked to Brumm in the Distant Village - possibly you visited the house without Grimmchild, or just never found it - it's the one left-down from the big one in which the weavers ask you to rest.