(not sure if I'm the first to notice)
If you select either reverse/hardcore modes in an existing save file and then start a new game, the mode will stay the same even though it hasn't been unlocked (a similar thing can be done in cuphead where you select the expert mode).
Maybe a hardcore run from the start is possible? I haven't tried, but theoretically it is
This happens even if you start a new game on a different savefile, or you must start in the same place?
Oh, I didn't understand your question at first. It can be any one of the three save files. I guess the mode is just stored globally and only changed when you press one of the buttons
Edit: I think it should be called the "Fresh Hardcore" glitch. Reverse is redundant pretty much (it is called Fresh Expert Glitch in cuphead speedrunning)
I don't even think it has to be a new save file. I think you can do this for any save file regardless of completion
I tried the entire game with this glitch. After beating level 20, the savefile looks like this:
Kinda funny
So yeah, fresh hardcore run is definitely possible. Alas, a full game run is much harder than usual hardcore difficulty. Some of the red puzzle pieces are just not designed with lack of checkpoints in mind.
I added new 3 misc categories, for doing a full game run in any of the main 3 categories with this glitch. I liked the idea too.