A few weeks ago I had a fan problem and bought a new fan that I couldn't return. It ended up being a busted ground wire to the fan. (So if you are close to Houston I'll make a deal on the fan)
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I bought the jeep after it was totaled and didn't notice this ground was mangled and hanging by a hair. There are about 6 ground wires crimped under 1 lug. When I checked the fan ground with a meter I had a good reading but it wasn't good enough to run the fan. The ground wire is bolted to the inner fender support behind the power steering reservoir so check it out.
If you want to do a few checks unplug the fan connector and check the two large terminals for 12V. The terminal should read with the key on or off, it doesn't matter. The 3rd wire is control and I was told by the service manager at IPAC Jeep in San Antonio that you can jumper that to +12v and the fan should run on high. He didn't know exactly the voltage but gave the example of 6V low and 8V medium. Since they are variable speed fans voltage on the control wire will vary.
$600 for a TIPM sounds about right if that ends up being the problem. The plugin relays are interchangeable so to test them just swap a couple around to make sure that isn't the problem.
Stan.