Before you pull out the aux fan, trace the wires from the fan.
It should go to a 2 pin connector.
Pull the connector out.
Apply 12V to 1 pin and -ve to the other pin (on the wires going to the fan).
If the fan spins, then it's ok.
Polarity doesn't matter coz the fan will spin either way depending on which pin you apply 12V.
Try this first.