Modelling Mechanical Eyelids?

Hey everyone, first post here and still pretty new to Blender and 3D modelling.
I’m recreating a robotic model for a game, and I’ve hit a brick wall when coming to make some eyelids.
The eyes are perfectly spherical, I’ve just never done this sort of thing before and have no idea how to approach it where things wont clip and overlap, instead stick perfectly to the eye. Most tutorials I’ve found are either human eyes or not for Blender 2.8.
Thanks for any help in advance!

And here’s what it should hopefully turn out like:
(At least it’s what I’m aiming for - these eyelids move smoothly in animation without any overlapping)