Call it static or call it buzz, but my neck pickup (bass pickup) on my 4001 buzzes when I play unless I rest a finger on it. Gotten worse over the years. Not as much a problem when playing live with all the ambient noise. A real problem when recording. Tried all kind of grounding and polarity switching. Same result. But rest a finger on it and it quits. Is it time to call it quits on the pickup and replace or is there another work around I'm missing?
Thanks,
Zephyl

Sounds like the ground wire from the back of the treble pickup which goes to the mounting ring (or back of bridge, depending on year) is broken.