I got the buzz to stop. As Simon suggested it seems to be that the nuts on the tuners had loosened. Five of the six were loose enough for the washer to rattle. McCreed gets a few points too because I put my ear up to the machines as well, but could still swear that I was hearing the rattle from the nut rather than the tuners.

Who would have thought that a machine nut might come loose after only 36 years? I can hear you thinking "pretty much everyone." I should probably write Mr. Gotoh a thank you letter that the machines haven't given me a lick of trouble in all this time, other than the need to adjust the tuner nut every 36 years or so.

Thank you!