the pwm signal from the ECU to the module is the command from the ECU to run the fan at whatever %age of signal its seeing.
e.g. to keep the fan off the ECU sends a 10% signal to the module, if all signal is lost the fans run direct at full power (failsafe) - this is the reason why new corolla will have the fan running at full speed with key on when the "trakker unit" cuts off power to the ECU. - exact same type of working here.
the module is just doing the heavy working, the fans are themselves PWM controlled - but they are higher amp hence controlled by the fan control module on the radiator. Its a very simple setup.
Most shops will have the mitsubishi scan tool, even the old launch X431 series of tools can do 2 way communications with this car.
reason to say this is because if the coolant sensor is not reading correct or the ac pressure sensor is not correct the ecu can never send the correct pwm command to the module. This can also be caused by an air bubble in the cyl head.
replacing the coolant sensor doesnt guarantee removal of airbubbles, i would recommend to stop throwing parts at it and get a correct diag done first.