Did you do this with the fan and engine running? 12.79V is battery voltage. You should have 13.5V or higher indicating the charging system is working.
I was thinking to measure the ground wire itself... So from neg batt ground to fan ground then to the engine. Any reading over .5 volt is trouble. (Wire resistance would show up as a voltage.) Since the readings are the same you have it covered though.
So any difference of 0.5V with the way you did it with stuff running...
If you unplug the fan motor does the idle improve? (While the fan is commanded on? Not sure if you can safely unplug it running though depending where the plug is.) This would eliminate any computer issues and keep you to the fan motor and it's wiring.
You are almost down to the wiggle test looking for loose wires and connections.