According to my service manual the fans are there for two purposes. One to cool the AC condenser and second to provide some engine cooling. There is another fan (belt drive and viscous clutch activated) behind the radiator that provides engine cooling as well. Both electric fans appear to be activated at the same time.
They can be activated by either a pressure sensor in the AC or by a temperature sensor in the engine.
I have never seen just one of mine running. I would check the connector first and then the fan. You should be able to disconnect it and apply 12 vdc to see if it will run.
Clay WA5NMR - Ex Snowbird - 1 year, Ex Full timer for 11 years - 2004 Winnebago Sightseer 35N Workhorse chassis. Honda Accord toad.