A custom C++ Maya deformer to handle cornea displacement along the lid line and surrounding mesh.
Running on the GPU to make it puppet friendly.

The deformer does both cornea displacement and automatic snapping of the eyelid to the input eyeball geometry.
The radius, strength and shape of the displacement can be adjusted via attributes and a shape ramp for a decent amount of control over the final look.
The eyelid snapping influence can be adjusted by weights.

I my experience, I’ve found that a setup like this allows artists to simplify their eye look shape workflow by allowing them to focus solely on the eye opening shape in general and the flesh movement around it. 
I find this helps a lot with iteration speed and eye shape network management.

For best results, the eyelids would be modelled without any cornea displacement baked in, allowing for it all to be done 100% dynamically by the deformer.
However, as that is often not possible in production (due to renders and presentations being done before any rig is in place), the deformer will store offsets against the current shape, allowing for that baked displacement to be removed during deformation.