Well, it sure seems like yours does have a thermocouple for some purpose in that case.
I might try watching it while manipulating the control knob to see if I could catch it in the act of misbehaving; maybe that would give some clue as to what's going on. I kind of doubt it's the thermocouple, assuming it's being used as a safety for the pilot, since I would expect it to be heated more when the main burner is burning rather than less. I would tend to expect trouble with it to mainfest itself more in the pilot not being able to be lit or not staying lit when sitting and the main burner isn't yet on. I'm by no means an appliance expert, however.