Anime Eye Rig Difficulties

Alfax

Hey there! I've been working on an anime character for a friend so they can use it on VRChat and FaceRig, and I'm having some trouble constraining the pupils to the eyeballs in a way that makes them follow the latter's shape. I've seen a couple tutorials on YouTube about how to do it but this is my first time working with non-spherical eyeballs and I'm not quite sure what could be going wrong. As stated in this video, I could try using a geometry constraint, followed by a normal constraint. However the moment I use the normal constraint, the pupil rotates and gets stuck in a different position.

It does follow the eyeball's geometry, but the pupil doesn't stick to its surface after using shrinkwrap due to part of the geometry being stuck inside. I realise this is probably a very silly problem but I feel quite out of my element trying to solve this on my own, hahahah. There's probably a better way to do this, and I was tempted to try the animated texture rig some people seem to achieve in Blender, but I'm not sure that would be compatible with FaceRig