Hi guys, Thunderbucker here. The usual reason an electric bass or guitar feeds back is due to the pickups, not the wood (an acoustic instrument can feedback due to the sound board being moved by the amp sound, just as the string motion would)
Pickup feedback is caused by something in the magnetic field of the pickup being able to move. Remember that the pickup works because the iron string is moving in a magnetic field, and that there is a coil of wire that senses the changing magnetic field. And either changing the magnetic field, or moving a coil in it (the principal that a generator uses to make voltage and current) can cause an output.
So if anything magnetic can be moved by the amp sound (this can be the metal pickup can, nickel silver is slightly magnetic), or if any of the coils can move, then the pickup can become microphonic, that is, behave like a microphone. and of course, mics can feedback.
The most common cause is the potting (or lack thereof) of the coils. Usually, the coils are wax potted (dipped in molten wax for 15-30 minutes, sometimes with a vacuum pulled to help get the wax into all the crevices). You can see this in the Seymour Duncan you tube tour. This is time consuming and messy, so companies often try to cut corners on this. When CBS bought Fender, it was one of the first processes they cut, as a result, post CBS guitars fedback badly unitil they realized they had to bring back the potting process. I had a CBS tele with this problem. Sounded great, squealed like a pig.
You can test pickups for microphonics by tapping lightly on the pickup with something non-magnetic (don't use a screwdriver!). A wooden rod would be ideal (don't hit the strings, hold them very still). Even with a well potted pickup, you will still hear some of the tapping come out of the amp. But this test will clearly distinguish a very microphonic pickup from a much quieter one.
