I agee that I'm not sure that I have a problem...I've just never encountered this in over 20 years of doing setup and repair work on my basses an those of friends.
To answer the first question, no, it doesn't sound any different when I play, except that this particular pole piece seems to have to be set higher than I think is normal for equal volume.
I was very careful about not touching the ruler to any ground source. When I touched a string (grounded to the bridge with bridge also being grounded to the output jack), there is no change, just a crackling static noise and a 60 cycle hum if I move the ruler around. Just for fun, I took another metal object (a screwdriver) and tried the same thing...it didn't matter if I touch the pole piece while grasping the plastic handle of the screwdriver or if I was holding onto the metal shaft.
This is just a weird one and has me stumped. I would think that the pole pieces would all be grounded, by contact with the metal pickup bobbin. It's almost like this particular one is not, for some reason. Starting to wonder if the pole piece is glued into the bobbin and not making contact because of a heavy coating of glue.
I'll have to dissect it and look some more. I'm the type that won't rest until I find out why...even if it is a trivial issue.
