OK, here's what I was told by the dealer this morning:
There is a TSB on this. Just about all the Rams with electrical folding mirrors have this problem. The problem is an internal tension wire that folds and unfolds the mirror. The "fix" is to fold and unfold the mirrors 5 times in a row using the switch. This supposedly resets the tension and corrects the shake. This may or may not work and the dealer suggested simply folding the mirrors every time you park might also help.
The small access panel under the mirror is not for tightening the internals. Don't bother, there is nothing to tighten. Should you order a replacement mirror.....it will do the same thing.
You might try looking at the TSB for more information. I didn't get the number.
I asked if "I patted my head and rubbed my stomach at the same time, would that help?" They were not amused.