Are you testing continuity at the ring of the jack?

The best antennas for picking up RF noise are the pickups and the strings, I think. So best bet is you have a bad ground to the bridge or one of the pickup shielding wires.

I have heard a ground loop can also cause this if you have components with multiple paths to ground, but I have never actually had this problem. Best to check the easy stuff first ;-)

Sent from my ONEPLUS A3000 using Tapatalk