wow - my little shop in khi had oscope and a plethora of other weird tools I used, anyway - cant expect everyone to have them.
to test the module - you have to wait, the ecu doesnt immediately ramp up the speed because you pressed the A/C button, the system high pressure sensor sends its info the ECU which then sends a signal to the module to spin the fans faster. It happens gradually.
in some cases you wont ever be able to see the fans go full speed (e.g. bonnet open in night time while testing A/C in recirc mode)
let it do its thing, if you see the engine is overheating or the module is not controlling speed at all or is sticking then its bad (which it usually is as the module mitsubishi use is garbage) - why cant they do what mercedes benz used, a really good solid state module made by siemens and installed neatly in a place where no water splashes.
with a scan tool that can talk to mitsubishi (mister basheer), you can actually command the module to spin the fan speeds to full and back as one of the active tests (there are lots of them)
and you will be able to see what the ECU is seeing as coolant temperature and ac pressure and what is being commanded to the fan,