Remote start/power issue

[02Silverado]

Hi all! Girlfriends bad weather/dog hauler car has issues. When started with the remote, the interior never heats up with heat controls and blower set to max, and none of the gauges work. However, once she puts the key in and turns it on, heat works fine. Also, one day last week, they quit working on her. She tried shutting it off and restarting, to no avail.
When she got to my house, when I started it (3X in a row), everything was fine.
I suspect a relay failing, or a bad connection. She hasn't had it that long, so we don't know much history(bought from grandson when he joined the Army as a backup ride for **** weather. She just bought a 2019 Mustang GT convertible! Doesn't want to drive that in **** weather.
I do electronics for a living, so I'm up to the task. Just need some ideas where to look, and probably some wiring diagrams too.
My questions are...
1. How does remote start interface with rest of car. Is it part of the BCM, or is it a separate module?
2. Does the power circuit that feeds the gauges also feed the climate control system (manual unit).
3. I'm guessing the gauges are operated by the BCM like most other GM's of this vintage. Does BCM run the climate control system too?

 

[cheatah faheatah]

Vehicle year, model & trim might help illicit a response.

 

[Bronco Boy]

My questions are...
1. How does remote start interface with rest of car. Is it part of the BCM, or is it a separate module?

Separate module(s). Some may pull signals from the BCM after you tap into it via the alarms wiring.

Sounds like either the remote start is wired wrong, or you have an HVAC issue (which these cars are notorious for).