Of course they close their eyes, but where’s the eyelid? There’s no skin that folds up into itself, like humans have, that I can see. It’s just straight-up fur-covered cat face, and for the life of me, when they close their eyes I swear the skin and fur are just sort of morphing into the closed-eyes aspect. I looked and looked at my cat to get a handle on this, and all I can conclude is: no eyelids.
They don’t need the old human “roman shade” style eyelid, because they have that special
nictitating membrane or third eyelid to take care of protection and moisturizing needs. Their
regular eye-closing feature is custom designed for demonstrating superiority or condescension
by means of the half-close.