2012 Grand Caravan acts strangely when either the driver or passenger door is opened (ignition is OFF, and no key in). Here's what happens, EVERY time a door is opened: for a duration that seems to be at least 30 seconds, the rear defrost light flashes and the blend door actuator buzzes as it hunts back and forth (I've watched the blend door actuator in motion during this strange behavior, passenger side). It sounds like something is going to break, and I'm surprised nothing has, yet. This has been going on for years. I've tried 'resetting' the blend door actuator, no change. Should it not be the RECIRC damper that adjusts when the ignition is off?
NOTE: when I bought the van (used dealer) the passenger side AC / heat was not working properly, and the dealer committed to correcting that. Could it be that the used dealer re-flashed the controls, and messed them up? I think this all corresponded to the same time, but honestly can't recall that. I had had a few other issues with the used car dealer that I didn't think at the time of returning to him again with this issue...honestly thought it would go away on it's own.

 

The actuator that is closes to the glove box maybe the sound you are hearing. What you can do to verify the correct actuator is to unplug it. There are total of 3 actuators.