First. Have you
CONFIRMED that the cooling fan works on BOTH low and high speed? A good method is to run the fan directly from battery with a jumper. There should be an obvious speed difference between the LS and HS. There are three wires. Black goes to ground. Powering either of the other two wires will select the fan to run at LS or HS.
Does the fan come on when the AC is turned on? If not, then the odds favor that the low speed part of the fan is not working.
Want an easier way to test. Then get an ODB2 scanner with bi-directional capability. Using the ODB2 scanner you can command the high speed and low speed fan to turn on. This makes trouble shooting sooooooo much easier.
Here's some information on an affordable Windows based ODB2 solution.
ForScan ODB2 scanner w ELM327 USB
https://www.stangnet.com/mustang-forums/resources/forscan-odb2-scanner-w-elm327-usb.57/