So generic characters can enter battle more than once per phase. The question is does their ability activate every time they enter battle, or does something have to happen to them in order to reactivate (get reset or something).
So two examples:
Type 2 game: Generic Demon enters battle, is discarded then Gates of Hell is played to bring another copy of the generic character into battle. Does the second one trigger.
One of these generic self capture characters gets captured, released and added to battle a 2nd time. Does the character trigger again?