My Peavey Ultra Plus' resonance switch broke off and I need to replace it... I don't mind calling Peavey and trying to get a new part, but I'm just checking first if I can use a spare guitar part.

There are three modes. Tight. Medium. Loose.

So, I'm wondering if a Gibson style three way switch will work instead. It looks like it will fit. But I'm not exactly sure if it will work.
No, they're different types of switches. I'm not sure exactly what the Ultra Plus uses, but its definitely not the same sort of switch as a Gibson pickup selector switch.