The fan will turn on with the car's idling.
Have you tested for power to the switch? If there's power to the switch, and the switch works then the fan will come on.
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OK I finally fixed the problem although I don't even know what I did to fix it. I just took out the fan switch again and gave it a real good clean (there seemed to be some sort of calcium buildup on the probe)..so I used some vinegar and gave it a good scrub. Then gave the electrical contacts a squirt with contact cleaner, let it dry and re-assembled. It took quite a while for the fan to turn on but it did (around 15-20mins of idling).