Re: death of the humbucker
Maybe have a real close look at the end of the cable, where the shieded outer (braided) wire is pulled away and the inner insuated wire comes out from iniside it. Sometimes the tiniest hair of wire from the outer braiding can be floating about and contact the inner wire and cause a short that will give you this zero ohms reading. Also at that same point, really look close to see where the inner wire's insulation disappears into the outer braided wire....sometimes through too much heat from the iron , maybe one too many pickup swaps with a hefty iron, any excessive heat can damage the inner insulation just enough to allow the inner and outer conductors to make contact and again cause the short. If that is the case and you have enough wire length, you can cut that part away and make a fresh start and that would cure it. Also check the entire cable length by eye for damage, and have a close look at the end where it joins the pickup for any damage.
Often a pickup willl die by going open circuit rather than short circuit...in other words, the wire will break somewhere, often the fine wire of the coils themselves. That would give a reading of infinity on a meter, just like when you turn the meter on and don't touch the probes to each other or anything else. In your case, the reading of zero ohms is a short circuit, and although it could happen iside the pickup, if it has only been stored, it would probably be more likely that the cable is damaged.....which is far preferable because you have a better chance of being able to effect a repair. Let us know how you go....