Cooling fans only run when coolant sensor is unplugged?

Will the cooling fans come on when the A/C is on? There is a high and low speed relay that can cause this if one of them goes out we should also run the codes to make sure the PCM is okay. Here are two guides to help us get started on fixing the problem and the location of the relays in the images below:

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

and

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Also included are the cooling fan wiring diagrams so you can see how they work. Check out the images (below). Please let us know what you find. We are interested to see what it is.