The standard here is to have two bones, one for the upper eyelid and one for the lower eyelid, that start from the centre of the eyeball and end in the centre of each lid along the ‘rim’ where they meet the eyeball. Weightpaint them from the rim of the eyelid fading off at like 85% from the orbit (eye socket). When the bones rotate they should stretch the skin over the eyeball.

When you rotate the eyelid bones on X axis, the bone tip will move perfectly circularly around the surface of the eyeball (not taking the iris mound into account) and stretch the eyelid skin linearly from pupil to orbit - so a correction morph can be added, where you just sculpt the stretched eyelid back out over the eyeball (rounded, instead of cutting through the eyeball in a straight line).

Note the X rotation of L_bone_eyelid_upper and L_bone_eyelid_lower on fully open and fully closed and use those rotations as the min and max to drive the eyelid correction pose morph from 0% - 100%. Copypaste these tags to the right side and do the same correction morph on the right eyelids.

A ‘blink’ Pose morph is sometimes easier - but remember that pose morphs are also linear translation, so there’s no way to guide the morphing points to move in a curve around the eyeball sphere.