Hi Sarah, glad you found the part, GE use virtually the same thermostat in cycle defrost refrigerators into the 80s so they’re not too hard to find.
It’s basically a fairly common cycle defrost type thermostat. It’s clamp to the evaporator in the refrigerator section and needs to allow the evaporator temperature to warm up to mid 30s before it to let the compressor turned back on and then it cools down into the low teens or upper single digits before it shuts off the compressor.
Hope this thermostat fixes whatever problem it’s having.
John L