How to stop eyes clipping through head mesh?

So I created a character using MakeHuman and imported it with its rig into blender. I needed to create a way to control the pupil size so I modeled separate eyes and have the system working. However, when it comes to moving the eyes within the head, the eyes clip through the mesh no matter what I try. I’ve tried constraints and limits but nothing seems to work. I’ll attach the .blend file for more context.