This sounds like the clicking behind the glovebox:
The white and yellow "pods" switch the ACC system and the auxiliary pump. I believe the white one is the "master" ACC vacuum switch and the yellow is for the aux. pump. They do click when vacuum comes up and the system switches on. It seems like a vacuum leak could cause either switch to turn off/on.
The aux. pump will be on any time the temp is below 79 F and the ACC system is turned on.
Do you have a mity-vac type pump?
The amp is all solid state and doesn't have any clicky things. It's kind of like a transistor radio. You'll find it screwed to the metal (left center) plate in the picture. It has little square waffle looking holes in it and a plug with a bunch of wires.