There could be several things wrong and first are you sure that the magnet wire is 42 gauge? Sometimes if you buy surplus magnet wire the label might be wrong and that’s why it’s surplus! If the wire is old the insulation might be brittle and flake off as you are winding. This can happen to the older plain enamel or Formvar insulation’s. If you wind the bobbin too fast and have too much tension on the magnet wire the insulation can become exposed and short out to other turns in the coil. There are many reasons why the bobbin reads so low and my first thought was it was the wrong gauge magnet wire. You need to contact a magnet wire supplier and get a magnet wire chart that gives you specifications on each gauge of common magnet wire. I often measure ten feet (10′) and multiply by 100 to get “ohms per 1,000 feet. This will give you a more accurate reading than just measuring the diameter.

The bare magnet (copper) wire diameter can have minimal, nominal and maximum tolerances. It can also have the same tolerances for the insulation and build coating the magnet wire. Some insulation’s can have single, double (heavy) or even triple build or thickness of insulation coating the magnet wire. The coating keeps the magnet wire from shorting pre or post turns in a coil. When you wind the Fender style bobbin with 42 plain enamel, Formvar or other Poly insulation with 7800 to 8300 turns you should have a pickup that reads from 5.8k to 6.3k. There are so many variables such as magnet wire diameter, magnet wire resistance, tension, winding tolerances, temperature and winding speed to name a few. Another important factor is the tolerance of the ohm meter you are using. Is it analog or digital and are the batteries good! Do not touch the ends of the meter probes as your fingers can interfere with the results when reading the DC resistance of your pickups.