All good advice, so far (especially for the barmaids), but there's a good chance just retaping the windings will fix the problem. There's a chance it won't help of course, but worth a shot. A pickup coil that's microphonic, is generally so because of a loose coil or two (or fifty!). Tightly re-taping might just fix it. Just be vary careful when you remove the old tape. If you break any winding wire, it could be a problem. Also, there's no reason you can't swap the coils over, so for a quick fix, if it only makes the noise from your thumb, then when shifted to the g-d spot, you won't have the issue. Oh and you can use super glue on coils too.
If it's a vintage pickup or something worth a few bucks, please ignore all my advice
and take it to a reputable pickup winder for potting.