Even before I found this video, I was vaguely aware that Picard tugged at his shirt a lot, but watching him do it 130 times was more than I can bear. I admit I skipped ahead a few times.
What I found interesting was that, while Picard prefered the two-handed vertical pull, Riker, tended to do a one-side-other-side version
[Ode To The Picard Maneuver (With Data)] (Viewer #256,214)
Now that I think about it, didn’t Kirk used to do this a lot, too?