https://www.youtube.com/watch?v=-4eOpeJp9Jw

i made a kinda lazy youtube video on it but the concept is pretty simple, you need to have the eyes default state as spheres, they rotate as spheres, and then apply scaling after the rotation

1. spawn in a sphere, roughly (and uniformly) scale it down and place it in your eye cavity.
2. rotate it 90 degrees and apply the rotation/scale
3. spawn in an empty at the spheres origin
4. parent the sphere to the empty, you can now use that empty to scale and position the sphere as you need to make it fit within the socket
5. because the eye rotation happens BEFORE the eye is scaled to fit inside the eye, the eyes rotation is unaffected by it not being spherical

When recreating this effect with bones, you need eye.L / eye.R bones that are used to handle rotation, they must be parented to "eyeScale.L / eyeScale.R" or whatever name bones in the same position that handle the scaling. Scaling needs to happen after rotation or else the effect won't work

I recommend also duplicating just the iris part and scale it slightly outwards and keep your sclera static if you want to paint on shadows on the sclera/delete parts of the sclera that aren't seen or that are clipping with the mouth bag.