Hey David,
That's an odd issue and I don't understand the circuit enough to know what might cause that kind of oscillation. It could be a failing component; opamp, voltage regulator (if there is one), a failing capacitor... but of course is should not be happening. You already know about exercising pots and switches so try that first and let us know if that has any effect.
The noise that Greg was suggesting is the RF spew that cell phones blurt out when trying to connect to the closest tower. It's a wild sound that is easily picked up by any nearby guitar pickup but it usually only happens for a few seconds so probably not what you are describing.
Jimmy J
