Right controller firing by itself?

[BassGuitari]

I was playing Xenophobe tonight and the second player would keep jumping in on its own. Defenseless, Player 2 would get killed since there's no one controlling him. Then he'd come back again.

 

I also played a bit of Dark Chambers to see how far I could get on Expert difficulty (that game really needed a difficulty mode between "standard" and "expert," BTW), and when I'd die, the game immediately went to the "Level A" screen, and I know for a fact it wasn't me pushing a button by accident.

(FWIW there was no controller connected to jack #2 when these incidents occurred.)

Has anyone had this happen before? I'm really hoping it's not a controller chip or RAM starting to go, since I really don't need another thing to fix, nor do I want to buy another 7800 (although it would be a convenient reason to get a video modded system; I'm usually a preservationist when it comes to this kind of thing, but the 7800's stock RF output is truly abysmal).