GE GFE28GYNIFS Refrigerator not cooling

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Brand: GE
Model Number: GFE28GYNIFS
Main Symptom: Not cooling
What happens & when: Clicks then hums for about 5 seconds about every 2 minutes

Error Code (if any): no error codes
Parts or tests already tried: Not able to test without a multimeter, but un-installed start relay and noticed a rattle with light shaking. I’m thinking it that part, but the new part looks similar, but the connector posts are in a different location. I want to make sure that I connect the wire correctly. Black wire to the correct post and the white wire to the correct one.

The start relay part is WR07010131.
Photos / video link:

The start devise would likely need to be replaced.