Your temp control in the fresh food side should control the operation of the whole unit. The freezer knob just controls how much freezer air is diverted to keep the FF side cool. In operation this means that the compressor doesn't run unless the temp control in the FF side asks for it. Since all the cooling happens in the FZ side this control system should keep the FZ cold and was the standard way SXS units worked for 30 years.

You should not be experiencing such swings in temperature in the FZ. Look at the rear panel of the FZ for ice build up on the surface, your unit may not be defrosting properly. If there is significant ice build up you'll need to figure out why. It's probably the defrost heater. Or possibly the defrost timer.

The evaporator is behind the rear panel of the FZ, if there is ice on the front of the panel, then there is much more behind it, blocking airflow and causing the fluctuations.

If there is no ice build up another possibility is that the temp control is faulty. It is located in the FF side behind the knob.

At that age either is a possibility. Take a look at the back of the FZ and we'll go through how to proceed. If there is frost built up and you are motivated to pull the rear panel off, you could defrost the evap as much as possible and see if that stabilizes it, the frost will build back up in a week or so however.

UPDATE ...
The manual says the FZ and FF controls are as shown in the diagram below. But in my refrig the diagram is the reverse (the arrows and blacked out sections indicate that the L knob controls FF and the R knob controls FZ). Assuming that the diagram on the refrig is correct, the On/Off control is on the FZ control. It also explains the results that I reported earlier where the R knob controls FZ temp, while the FF stayed at 38 F.
Maybe GE changed their design protocol.

Mike

The forum software does not allow me to include the diagram. Sufficient to say that the markings in my refrig are the reverse of what is in the manual: the L (9-1) knob controls FF temp, while the R knob (0, 9-1) controls the FZ temp.

Mike

Thanks, all, for your help. I have now concluded that the problem is with the user, not the refrigerator.

Having figured out that the markings of the temperature control knobs is the reverse of what is in the manual, I am able to control FF temp to 39F (set at 1), and FZ temp to +/-0F (set at 6).

Moral: If you step on the brake and the car goes faster, do you have your foot on the brake?:)