Maybe someone with a 'clickable' Pabst can answer a question here: If you stop the fan with your fingers, does it sit still for a moment before restarting? Does it give little 'kicks' to try to spin up? If so, are they at the same repeat rate as the infamous 'Pabst click'?
I fully expect that the Pabst clicking should be electrical. My first guess would be something to do with startup circuits accidently kicking in at low RPM's or voltages. Maybe putting in a bigger cap in the right spot would alter that behavior. If I ever come across one I'll be sure to fool with it on my bench and tell all. I did a (too long post) about fan motors a while back in Fans that are noisy, whining or clicking
. It's not specifically about Pabst, but down near the end it gives some suggestions about strange low voltage electrically caused noise effects.