Is the fan on your mustang the same motor/torque/blade design/weight, etc.?
If you hot wire just the high speed circuit at the fan connector, you'll see just that circuit spin up - is that the same response as when you self-test?
No idea how to force test when no freon in circuit...I'd skip it.
When you pull the ECT, I believe that is low speed. The system is not designed to power high just on it's own, without low already having pre-spun the fan, but ECT sensor fail does run fan on an emergency basis, so...
As for repairing our IRCMs, the boards are printed circuit and the relays are electronic. If something has failed, I'd suspect a capacitor. If you're comfortable working board-level and sourcing those components, you should have no trouble. Details via search. Easier to just swap out, I think.
My opinion, tho, is that the IRCM is frequently/incorrectly faulted, when the issue is actually the fan connector/motor, ECT, ECT connector, air trapped at the ECT sensor, etc. I had a pin plunge in a new ECT sensor and not make connection when connected - spent way too much time looking at the ICRM before I found that
It's always been a connection/harness issue for me - now I have 4 spares that were originally faulted, but test ok now that I have a better process.
Good luck.