I know that all the built in borders are animated when the game is left idle. But is there any borders that are built into Super Game Boy animated? Would be neat if there were some.
Do you mean to ask if any Super Game Boy borders from a game are animated? If that's the question, I would say none of the games I have include idle/animated borders.
Yes, they do. The country home border slowly transitions to night, custom drawing border gets erased by a janitor and the movie theater eventually has an active audience. The last one is my favorite.