Plumb a vacuum line using your MightyVac on the climate control line (green tube) then see which of the buttons causes the sound. If it's isolated to one function it's closer to that flap system, but if more than 1 function causes the sound it may be more distant (i.e. closer to vacuum source).
There are also check valves under the dash, IIRC there is a white/black by the brake booster area under the dash.
This is assuming, of course, that it's linked to the AC system.
The vent pod is also behind the glove box if you want to try that route.