If that is really happening, then is has to be the some trigger further into the stage that is despawning the buttons, rather than it being just the entrance to the waiting room (where the locked closet is). I say that because I clearly recall entering that room, seeing the 3 lights above the closet, and then going back to search for the rest of the buttons and finding them, finally unlocking the door to the costume.
EDIT: So I tested it: I found one of the switches but didn't press it, then I advanced through the stage, actually going a good way past the room with the costume. Then I returned all the way back and the switch was still there, in the same place. I even used it, and the corresponding light was activated in the costume room. So I don't think there is any timer or despawning effect. These buttons are just really incredibly annoying to find, is all.