Two things;
- I'm not sure about this switch but most switches can be cleaned, you might have corroded contacts somewhere. Worth trying.
- David Schwab (I think he is SGD luterie or something here) have posted many good threads on pickups, I think you can find a good deal on ripper electronics and pickups on the music electronics forum.
and yes, if you get no reading with the pickup IN the circuit, it should be easy enough to check it out of the circuit.
But record your work, even 3 wires can slip out of your memory quite rapidly!