The "wiggly thing" is called the pendulum. It may look like an "updulum" since it sticks up instead of hanging (pending) down, but if you look inside, you'll find a larger "hangy-down" weight that looks more like what you'd expect. The "double pendulum" is a feature of virtually all mechanical metronomes, since a simple "swinging weight" of convenient size would require an extremely long pendulum to get the low "tick frequencies" needed. The lower weight is usually fairly wide, and it's the "resistance to rotation" (rotational moment of inertia) that provides the lower frequency with a short pendulum radius.

I don't find a "nomenclature" for the little movable weight other than the "adjuster."

You can find here aa fair A SHORT HISTORY OF METRONOMES.

If you want more detailed information, you probably will need to look at some of the "collectors" sites. I didn't find a good one, but Horological sites of interest looks like it might be a good place to play around at. (I haven't played there yet, so can't make any guarantees.) Lots of interesting looking links to be followed.

(Note that with my slow connection, this last site says "done" with a blank screen, but if you wait a bit it will finish loading.)

John