I will tell you what I have found, I have a 2000 GC and there is a module for the fan under the pass. side headlight on the fenderwell. I replaced mine three times
however it kept failing. I eventually hard wired my fan as well kind of a pain really but solved the problem. Hope it helps

Sounds like the same problem im having. My fan doesn't come on when I unplug the CTS or with the A/Con which mine doesn't work. Or if the temp gets high. I can jump it and the fan is good. I put a new relay in and still getting the code for a bad fan relay. I pulled the relay and got the fan to come in my powering up the prong with my power probe.