Like the title says, my cutlass started causing a rumble noise through my amp a while back. I couldn't find any information about it online, so here I am!  Here's what I've tested so far:
Edit: SSS pickups
	
		
			
		
		
	
			
			- It is independent of the pickup selector, tone knob, and volume knob
 - It doesn't happen with my other guitar
 - Playing it doesn't affect the noise at all (for better or worse)
 - I checked the jack and battery cables from the back, which seem to be fine
 - I think I tried two different batteries, but I'm not sure (was a while ago) so I will be doing again that later to double-check
 
Edit: SSS pickups