Hello!
I’m not an expert in the field, but Pxy-Gnomes helped me a lot by sharing the eye rig for non-sperical eyes tutorial. I believe that the rig Pxy-Gnomes is describing in this post is a newer version of this one 2D Eyes-Track Rig Tutorial. At the end of the second video, it is explained how Pxy-Gnomes connects bones with material using Warp modifier (by filling “object to” with Armature and then “Bone to” with relevant bone for example).
I hope this is relevant
Cheers