I would take the cap out first and check whether the problem is still there. If it goes away then replace the cap. If the problem persists it has nothing to do with the cap. I would look to the pot as the next possible culprit. Swap it for a known good one. If it goes away you're done. If not, the problem is in the pickup (very unlikely) or in the pickup leads.
You could also do the following: swap the bridge and neck pickup leads, i.e. solder the neck pickup hot to the bridge pickup volume input lug and vice versa. If the problem is now with the neck pickup then it's either the pot or the cap. If the problem follows the bridge pickup it may be a kink in the bridge pickup's hot lead. Maybe it would then be possible to shorten the pickup wire.
Good luck
Stephan