Your fridge has simple controls....no electronics/no control modules/no circuit boards.
Just ON/OFF-----GAS/Electric Thermostat----Piezo Lighter
Sounds like thermostat is not turning electric element off ----allowing it to run continuously
Thermostat should turn element ON/OFF when temp set point is reached.
In gas mode it would shut down gas valve and go to bypass when temp set point reached then increase flame as fridge temp increases.
Check selector switch continuity
With AC wires removed......and AC Selected
Continuity between 4L and 4A
Continuity between 5N and 5A
Then Check thermostat continuity