I do not think the problem caused by the defrost timer.
Most likely the failure suspect is the defrost thermostat.
The defrost timer is just a timer. If there is nothing wrong with the defrost cycle goes "on" and "off" then there is nothing with the defrost timer.
On other side the defrost thermostat opens or closes the circuit to the defrost heater according to the evaporator temperature and most likely it stuck in the "closed" position.
- The part number for the defrost thermostat is AP2639498
Here are the break down diagrams for the GE refrigerator Model TFHA22RRAAD