once you've unlocked
head into the newly unlocked level, character and settings don't matter. all you can do is walk straight up into a flashy looking statue thing to bring up a dialogue box. choose "too hard" to get the trumpet, which unlocks Endless Mode.
if you instead chose "too easy", you get
instead, which unlocks Inverse Mode, and Eudaimonia Machine will disappear from the level select. to get it back, just start a level with inverse mode turned on, and quit out of it. Eudaimonia will reappear and you can go back in to choose the remaining option and get the trumpet.