What we know with certainty is, it isn’t the relays. (The harness looks fine to me.)
As
@Rocket Man said in post #9, if you had access to a Tech2 (not sure if other bidirectional tools can do the same, they very well may) you could command the fans on via the PCM. If that doesn’t turn them on it could indicate issue with PCM. Otherwise, might be a myriad of issues not allowing the the PCM to think they need to be turned on.
BTW, tossing a random PCM in and running the truck is potentially disastrous. You would need to know what OS and calibrations are on this spare and that they match what came from the factory.
Good luck.