The use of a test meter that will measure voltage is the only way to nail this one Mr. Matthews. Without one you really are trying to find this fault with one arm tied behind your back and blindfolded.Mr Matthews wrote: Not with a volt tester or anything, but as none of the connections looked disturbed or blackened, I just dismissed that notion.
With a voltmeter, there are a few tests you can do to confirm if it is the supply or the fan run signal from the aircon ECU. The details are in This Thread. You can also get meter probes right on the motor supply.
Maplin or any DIY store do simple, basic multimeters that will serve the purpose very cheaply.