P-pass pickup with three wires?

I believe the average DCR for a Split P-Bass pickup is around 11.0k ohms, so your pickup is on the hot side. The third wire could be for shielding, but it’s hard to say without knowing exactly what pickup you have.

 

Maybe a tad hot, but definitely still in the ball park for a P-style pickup. The bigger question: are both halves of the pickup the same so that it functions properly.

 

A pic of the pickup would definitely be helpful.

 

Could be a ground wire. What is the dc resistance between one of the pole pieces and the third wire? If it's zero, then it’s a ground wire.

 

All pickups are wound on machines to a number of turns of whatever wire is put on the bobbin, commonly #42AWG formvar or plain enamel for vintage-style pickups, depending on the era and nuance of tone being sought; other wire and other winding formulas are used for different tones. (Just talking basics, not the geometry of the bobbin, magnets, etc. for this post) If anything about the winding machine varies during the winding: speed, tension, counter shut-off, etc., then the wound bobbins will not have the same electronic characteristics, and will not be completely humbucking.