I thought I had this for a while but now can not repeat it. I want to simply wiggle my line by animating the vertices within. I have a line with 4 vertices, and move the whole line by animating position. Then after the line has moved, I try to move the vertices with the selection tool and the whole line moves. I have tried clicking the stopwatch in the "path" category, sometimes they do move, but they don't animate, they just permanently change the shape of the line.
Maybe it is just late.
To animate vertices you just have to turn on the stopwatch for the mask path or turn on the auto animate button, then use the direct selection to carefully click directly on a vertex and drag it to it's new position. If you double click you'll select all vertices and get a transform bounding box which will move all points. The ESC key will deselect, the enter key will also deselect.
You may also use the pen tool and the Cmnd/Ctrl (mac/windows) key to select vertices and edit their position or change the bezier handles. There's a good section in the help files on drawing and editing masks. Take a quick look there and you'll be fine.
When animating, at each new keyframe all vertices will be selected/ the entire mask active. You need to explicitly click on the point you want to animate and may also need to pro-actively deselect the others. Otherwise keyframing the mask shape property is the correct way to go, so nothing wrong there...