(A longer segment from this scene can be seen on youtube here)
I tracked the tip of the gun. As an instrument, it magnifies a motion that is complex primarily in rotation; the translation would be fairly smooth. Incidentally, if this were animated it would make sense to animate this with a constraint, and it would be important to locate the COG somewhere around the middle of the gun rather than his wrist.
I think a key think to notice from this is that the shaky motion is fairly random. It does hold for about 2 frames and jump in about 1 frame, so there's a slight clustering of points. But it's more "white noise" than "pure tone" vibration.