Why can't we half-close our eyes?
The motion of the eyelid is driven by the levator palpebrae superioris, i.e. elevating muscle of upper eyelid, and it can be positioned to the intermediate, half-closed positions. At least I can do it.

Yes, this muscle tends to shake or oscillate simply because it's a very weak muscle. It's similar with the muscles controlling the motion of the little finger (or ring finger). Vibration and "noise" is present in all muscles but the stronger muscle you have, the more accurately the random motion is averaged out.

If you connected $N$ eyelid muscles so that they move in unison, the noisy vibrations would be reduced by the factor of $\frac{1}{\sqrt{N}}$. This is the well-known scaling of the statistical errors in physics etc.

I would think that this question was totally appropriate at the Physics Stack Exchange.