Little switch on IP pump is two fold. On the 3 speed transmissions (I don't have experience with 4 speed rigs) it controls the kick-down solenoid AND triggers the TDM to DISengage the fan to go for a swim.
Should give you about 20 seconds to get wet before fan comes back on....
IF the engine is above 190 ish ++ and fan temperature switch (in water crossover) is working properly.
(Note) fan temp switch is an OPEN switch when 220 ish hot or fan is running. Closes at 190 ish and below so fan should be off. This is the only switch that cycles fan on and off while happily going down the road.
OR
The kick-down switch (side of IP) triggers (momentary 24 volt pulse) to start the TDM to begin the 20 second +/- swim feature applying power to the Cadillac valve which disengages fan even if the engine is hot, overriding the temp switch. Confusing as heck, but it works well.
To pass grand-ma, the kick-down switch needs to be fully engaged, peddle to the metal to HOLD the solenoid engaged on the valve body in the transmission. Added bonus TDM get the trigger pulse too and off you go with a little more HP. All things working properly of course.
Those kick-down switches do go bad or could be out of adjustment. Pull one of the wires to it to check if fan STILL follows throttle position.
Does the transmission down shift correctly at peddle to the metal?
Question for you. Have you been reading the little book? >
https://hummerhuren.files.wordpress.com/2013/01/hmmwv_test-diagnostics.pdf
Taking a survey to better serve, CAMO
An after thought... saw a picture posted a couple weeks back with a new fan temp switch that looked like a knockoff. SS was having fan issues. Just wondering here. You can set you clock by the humv posts. FAN problems in the summer. Start boxes in the winter.