I was pulling my hair out with one of my basses, on another strange resonance kind of thing, and finally after several months, by accident, I pressed my hand on the pickguard in a certain spot, and the funny resonance all went away.
Thanks for the link dmusic - was a very interesting read.
Today I compared my bass against a recent model Fender jazz. There was definitely a small 'wobble' around the 15th fret, but nowhere near as pronounced as mine. When I took the bass to my teacher he said I'm probably becoming obsessed with a minor issue!