Just a word that agree with the assessment of a leaky diaphragm.

It is probably a vacuum motor, one of three under there, that runs off a vacuum bottle in the bottom of the center console. That is why it probably takes 20 seconds to fill its own contents with atmospheric air pressure.

Two of these operate the floor vents that keep your tootsies ventilated if selected. They probably default to open.
Check and see if you have the floor button pushed in and the noise stops happening when you shut down.

With no vacuum, the fresh air one in the center behind the console defaults relaxed, to make sure you get fresh air. It's for safety reasons, to keep any sleepy moments to a minimum.

Good news is, eventually, it will stop creeping closed and start doing it right after you shut down. Just one thump. Sometimes it quits all together.

Bad news is, it will effect idle smoothness, a little bit, during a start up because the engine needs to pull a vacuum again on the reserve bottle.

I surely hope for you that it's a foot vent and not the center console vent door motor.
It's buried in the very back at the top!
You will want to do what I did, to keep from pulling that console.

I put a string to the door to hold it shut up against the heater housing so I could get fresh air in all the time.
I release the string to recirculate cabin air as a spring pulls it back into that default position with no vacuum available.
I plugged off the line going to that vacuum motor, until some day, way in the future!

I will wait until a fan motor or the heater core goes out!
Maybe just the heater core because either can be a gruesome job!


Phil