Fans, and electric motors in general, have a very high starting current. If jumping across the temp switch makes the fan run every time then I think you’ve identified a bad switch. If you have an ohm meter handy you could let the bike heat up and disconnect the switch and throw the ohm meter across the switch terminals. It wouldn’t take more than a few ohms of resistance to limit the starting current to the point the fan won’t start running but would keep running once started. I did take a Beta fan into the lab once to measure the running current and it was about 0.5 amp but if I limited the supply to anything under 10 amps the fan would not start. I think you’re up for a new switch.