Help: MM Cutlass Causing Intermittent Rumble

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:

• 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

Only thing I haven’t done yet is take off anything from the front to troubleshoot. Wanted to see if anyone had advice first. I can record the sound and upload it in a zip file if needed.

Edit: SSS pickups