What year model? If it is a late model with dual air temp controls, it is most likely a temp door actuator that is attempting to rehome itself after key off. If that is the case, the actuator will need to be replaced. Of course, that is assuming that it is, indeed, a late model. That wouldn't apply to a 1965
ASE & GM certified master technician, and no, I don't think I know it all.
We play with our 1958-'76 Impalas here as aside from myself few have anything newer than that here. As you have already received one reply I will point out that you are welcome here, but aside from a ASE tech still working in the trade few of us will have any answers to your questions regarding late model wrong wheel drive cars.