The time delay module as noting to do with temperature. It allows for a twenty second +/- window to disengage the fan during;
1: an attempt to force a down shift (peddle to the metal and kick down switch correct and transmission solenoid does its thing) getting a little more HP out out of the engine to make the shift and get out of it way.
or 2: when entering deep water by peddle to the metal quickly, fan disengages as not to turn the fan into a propeller with 20 sec to get in the water, should the fan have been engaged. Hit the water running good chance of sending shards of plastic fan parts to the bottom. Once it the water ya need to tippie toe across. HUMMWV fans not know to be very good propellers.
The temperature switch in the water crossover controls the cycling of on or off. Yes, you can unplug the TDM and run fan continuous. (fail / default mode) any gain is questionable. Let it do its thing IMO.
Loss of power to the Cadillac valve, fan runs. Assuming all the parts are playing nice.
Tubro engines can run a bit higher, but should cycle OK. Running at temperature is best for diesels.
Gauges are slow to react or have a bit of hysteresis and in many cases not known for accuracy. Make a mental note of the highs and low cycles point and that's your HUMMWV temperature health. Anything out of your norm, time to see the doctor. LOL
Take a lookie here >
https://hummerhuren.files.wordpress.com/2013/01/hmmwv_test-diagnostics.pdf < This is the manual that didn't come with these rigs. Answers all the easy stuff for FREE.
Hope this help. Good luck.
No hot flashes, running cool, CAMO