UPDATE:
Got the new parallel cable and the generators work fine. I was able to do some testing.
I owe Doug an apology. My thermostat has apparently been working fine the whole time, I just wasn't patient enough. It seems that even if your AC has been off (like mine), any time you put it to the auto positions, it automatically uses the 3-minute delay. I placed it in auto and waited and about 3 minutes later, it fired up and ran fine.
So, as far as what is germane to this topic, it seems my thermostat is fine. For the other gentleman in this thread that was having the same problem, maybe just try waiting 3 minutes. If you have done that, then maybe you have another problem but when you're waiting for your AC to come on in a hot trailer, 3 minutes seems like an eternity.
I also noticed during testing last night that my thermostat does not have the "Built in Time Delay and Fuse Protection" text on the front like the pictures I linked. It obviously has the time delay, but no warning.
Check my other thread for more information but unfortunately, the first start was the only time I was able to get the AC to come on.
