i agree about the bad switches, and your doubt since it occurs when the key is out. It might be a combination of the ignition switch and a bad switch since there should be no power to the fan with the ignition off.

Does this model have a 'run-hot' function whereby the aux fan keeps running at very high engine temp, even after the car has been switched off ? maybe that switch is the culprit ....

my 0.02's worth
L