macowi, welcome to the forum. Sorry to hear about your problem. I don't recall this ever being discussed on this forum.
I was hoping that someone experienced with this would chime in.
I cannot imagine that continuous running of the coolant pump is normal, nor that Mitsu would have made such a design change so late in the car's production run.
Looking at the Mitsu workshop manual, they devote a full section (14) to the cooling system. Sadly, the only two faults they identify are a coolant leak and overheating, although they do offer a procedure for testing the water pump relay which is located in what Mitsu calls the "Relay Box". I think it's the fusebox under the bonnet below the brake vacuum booster (LHD cars). A stuck relay could result in continuous running of the pump.
There is a temperature sensor located externally in the forward right corner of he MCU inverter. It has a connector that can be disconnected. Their testing procedure involves removing the sensor, immersing it in water and they offer the following readings:
0°C 5.1kΩ-6.5kΩ
20°C 2.1kΩ-2.7kΩ
40°C 0.9kΩ-1.3kΩ
60°C 0.48kΩ-0.68kΩ
80°C 0.26kΩ-0.36kΩ
I wouldn't bother going to the trouble of removing the sensor but would simply try to probe it in situ. I think that a shorted sensor would result in continuous running of the pump.
The cooling pump running has always mystified me, as, even when the car is cold, it cycles when the car is charging and before the coolant has even had a chance to warm up. So, speculating, I think there also a separate timer for the pump, independent of temperature. Anyone?
So, may I suggest that you get out your multimeter, and good hunting (and good luck)!