I did not think a P-Bass needed shielding but I figured I would do this bass while I was doing the Foundation and Foundation S shielding.
Checked the bridge to the output jack sleeve ground for continuity and it shows continuity.
I did replace the output jack, Peavey had a "switched 1/4" jack" in there and the tip and switch were wired and not the ground (sleeve) terminal which I believe is uncorrect.
After the pickup magnets were glued and dry and the pickups were back in, the signal was intermittent until I put the new jack in, now it makes noise reliably but with hum.
The jack was not a Switchcraft like some other Peavey's I've seen, and the pots are not CTS either which maybe Peavey never used.
I am thinking they were maybe using Peerless jacks at the time, I can't tell the brand of pots but they are full sized and maybe are Alpha, I think they say JS on the back of them.
I will go through all the wires and solder points and see if I can locate the issue.
Since 2 pots, some wire, and a cap are all so cheap - and it sounds like you know what to do with them - I would probably disconnect the pickup and hook it directly to the output jack, just to verify that the hum is gone. If so, then it must be in the pots or wiring, and so I would just put new pots, wire, and a new cap in and be done with it.