I have a similar problem to the top. I also have a 2001 f350 with a 7.3.
In my case the dash a/c vents never work anymore. They were working yesterday then just abruptly stopped. The defrost vents still work and they still blow cold air.
As for the vacuum pump it turns on immediately when the key is turned to on with engine off.
Another issue is a few days ago my mechanic friend noticed that a vacuum line near the pump that seems to run itself under the engine was cut. He reattached the lines together with the plastic seal piece and things ran fine. Except my gas mileage got a little worse. That was several days before this new problem. The vacuum line he fiddled with does not connect to the vacuum pump itself. It originates at what looks like a solenoid or something of the kind NEAR the vacuum pump.
I'm not having any other issues at this time. Breaks working fine. Barely have to tap them to make the truck stop.
Truck is 4 wheel drive but with manual hubs also. In the cabin it just has a three way selector switch between 2wd, 4w low, and 4w high.