The fact that you mentioned the A/C tells me you think it is an air door in the HVAC system? If that is case then I would agree however, can you get a recording of the noise so that we can hear it?
The fact that this start when you open the door would make you think it is a relay but hearing it should help determine that.
On your truck, the HVAC control module will run the doors through an actuator test which is how it learns the stopping points. It is unclear when it does this test but it very well could be as soon as you open the door so that by the time you start the vehicle that test is completed.
Let us know if you can get a recording of this and we can go from there. Thanks
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Sunday, January 10th, 2021 AT 3:20 PM