It definitely happens more than once after the engine is turn off. The van hasn't run in several weeks now, but I hear it just about every day since I'm working in the van a lot. Maybe 2-3 times a day max, depending on how much time I spend in the van. It isn't loud, so it would be easy to miss in a city noise environment. But we live out in the woods where it's dead quiet much of the time (that or chain saws). I'm more curious than worried.
EDIT: OK, I just did some more googling, outside the forum and PMs this time. Similar under-dash noises are common in Dodge Ram trucks. The consensus is that most are normal. The HVAC blend door seems to be the primary culprit. But I still couldn't find a reason for it's continued/repeated operation even when the engine is off.
I even found
, but not mine. The videos sound more like hammering or gears stripping. Mine is a continuous servo whine that changes pitch at the end as it meets resistance. Maybe the blend doors in the videos are jammed. Something to look forward to, eh?