1987 Toyota Corolla Electronics Problem

The radiator fan on my brother's car doesn't seem to work at all. It works fine when directly connected to the battery, but even when I try removing the plug from the thermostat switch (to test if it works permanently), it doesn't.

*** Could be the engine temperature gauge switch or coolant temperature sensor/fan relay

I'm not sure if this could be adding to the problem, but say if you were to pull out the battery & place another one whilst the engine is running on idle, the car stalls (where as on a normal car, the engine wouldn't cut out).

The old says if it continues to run the alty is good? For me