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Did they mention which actuator? The defrost or mode? I can give idea but it would be helpful to know which one.
Also, is this a repair you might be attempting yourself? If it is the mode actuator, it requires a few tools and is easier with small hands (tight area behind dash) but again, it does not require major disassembly.
The actuator is available separately and is readily available at any gm dealer.
It is a bit tight but does NOT require dash removal.
I don't have access to a parts database but ANY gm dealer can look it up for you by you giving them your vin number to make sure it is the correct part for your particular vehicle. I can't tell what he turned as I wasn't there but that is what makes sense. Turning the mode actuator shaft. Again, it's difficult without having a "hands on" diagnosis but it doesn't sound correct to me based on the information I am hearing. If the internal door itself were broken then yes... the dash would have to come out. If it is simply the actuator... which it is most all of the time... then it is removing the glove box... .removing three screws on the actuator and replacing it, then recalibrating the system which can be done by a scan tool or by disconnecting the battery for several minutes which will cause the controller to relearn the door positions.