Hi @ephraimschmitt
The compressor should only stop when the set operating temps in the refrigerator and the freezer have been reached or if the refrigerator is in a defrost cycle.
It may take some time to get to the set operating temp of 0°F in the freezer from where it started from
Here's the [https://f01.justanswer.com/smitty1486/29004ff2-7086-47bb-95ec-f39e757367d4_PFCS1PJYASS_Tech_Sheet.pdf|tech sheet] for the refrigerator.
It shows that the compressor is turned on by the control board via an [https://www.amazon.com/General-Electric-WR49X10283-Refrigerator-Inverter/dp/B00LQDI048|inverter board part # GE WR49X10283], (example only as it has a good view of the board).
It changes the 120V AC supply to 230V supply presumably to conform to the specifications of the compressor.
Are you using the temp displays as shown on the control panel? If so try placing an appropriate thermometer in the freezer compartment and check the temp, in case the display is giving a faulty reading.
If the display temp readings are accurate and the compressor is not operating and it isn't in a defrost cycle, then the problem is either in the inverter board or the control board.
By "flipping the switch" if you meant the power outlet switch then it seems that by doing this it has "reset " the control board and the compressor started again.
It does seem as though it is related to the defrost cycle though. Check if the compressor has stopped for more the 20-25 minutes. This is the approx length of time of a defrost cycle.
You have replaced the defrost thermostat, but all that does is disconnect the defrost heater circuit, so it may be the control board.