Are you referring the the engine cooling fan? I show you have a fan clutch which is heat activated with a viscous clutch.
If this is the case, then that is odd that the alternator would only charge when this is on as they clearly have nothing to do with each other.
However, I would start with checking the voltage coming from the PCM to the alternator to make sure it is commanding it on.
https://www.2carpros.com/articles/how-to-check-wiring
Below is the wiring diagram to help with this. It may be as simple as a PCM issue but let's start with this. Let me know if you have questions.
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Monday, March 15th, 2021 AT 6:35 PM