Hey Andy, I can't pull a beer or soda out of that fridge without thinking of you! Thanks again for rescuing it! If David (Marler) had his way, the fridge would have followed him to Tucson but it's not going anywhere, I can assure you of that!
Joseph, you don't see food because it's my designated beverage (and sometimes overflow) fridge.
John, good luck finding OEM control for your fridge. The aftermarket one I have is working fine, but OEM would have been preferred, as the mounting would be more solid. If you decide to go with an aftermarket one (Larry at Modern Parts might still have one in stock) I can give you some pointers on how to modify it (with provided parts) and make it work just like the original. The controls seem to be the weak link on GE fridges of this era. Mine did the same thing; wouldn't shut off. I had the aftermarket control here waiting, so took appropriate action and the fridge has been fine ever since.
Nate and I opened up the old control but couldn't really see any obvious issues with it. Otherwise, I would have preferred to repair that control and continue to use it. If a visual check of your control reveals the trouble, I can perhaps provide parts from mine to fix yours.