The deal w/the fan motor is that there are two windings/speed circuits...one for low speed and one for high. High draws so much current on spin up that the circuit is designed so it always/only comes online after the fan has first been spun up using the speed circuit. On high, both circuits are lit.
There are ways to modify the fan circuit so it always runs, but that's not something you've described so far, unless it used to do that and now, for some reason, it doesn't. I can imagine doing that mod the wrong way and having fan motor, and at least IRCM issues, sometime down the road. Speaking of which, why is there a new IRCM in the mix now?
I'd want to know what's going under that tape and specifically why a repair was needed/done in the first place.
What I've been trying to help you troubleshoot so far involves an unmolested fan, harness, connector, etc. No telling where to go next if that means a franken-fan circuit