After 2 years and a simple Wikipedia search, I think I've answered my own question about why induction pickups seem to be sensitive to vibration. I've highlighted the important sentence in red:
http://en.wikipedia.org/wiki/InductorAir core inductor
The term air core coil describes an inductor that does not use a magnetic core made of a ferromagnetic material. The term refers to coils wound on plastic, ceramic, or other nonmagnetic forms, as well as those that actually have air inside the windings. Air core coils have lower inductance than ferromagnetic core coils, but are often used at high frequencies because they are free from energy losses called core losses that occur in ferromagnetic cores, which increase with frequency. A side effect that can occur in air core coils in which the winding is not rigidly supported on a form is 'microphony': mechanical vibration of the windings can cause variations in the inductance.
The telephone pickups that I've opened do have a mild steel core so they are not air core inductors
but the actual wire coil itself is wound around a plastic bobbin, sometimes loosely. The wire is not coated with something like lacquer or varnish to make the coil a single solid mass, so the windings can vibrate. That causes a change in the inductance which in turn changes the induced current going into the recorder.
The same Wikipedia article says:
Core materials with a higher permeability than air increase the magnetic field and confine it closely to the inductor, thereby increasing the inductance.
Plain steel has a relative permeability of 100 and air has a relative permeability of 1 (
http://en.wikipedia.org/wiki/Permeability_(electromagnetism)) so if I remove the mild steel core from a pickup, the pickup's sensitivity should drop. And if I replace the steel core with a Permalloy core (relative permeability of about 8,000 to 100,000 depending on the alloy), the sensitivity should increase.
Something to try on a rainy day...
