I have a 1998 gmc 2500 with a vent door that keeps opening and closing. it is the vent door that changes the fresh air to recirculated.It opens and closes by itself with the heat, air, even when the system is off. If the air is on the compressor will click on and off as well. I also noticed that the heater core is always warm. figured it might be the switch or a relay.
Sounds like a vauum related problem; one-way valve, vacuum hose leak, vacuum pod leak, etc.
You’re just going to have to start the leak diagnosis process and see where it goes as there is no way of determining that from here.
There might be some kind of electronic climate control module.
Often these little ‘black box’ jobs have a pc-board inside that develop cracks in their solder joints.
A chat with the parts dept. at the dealer is one way to find out what’s what.