Question What is the best way to animate and control 2D textures on 3D models for character eye movement?

I'm trying to make simple animated eyes and mouths for my characters, and I want my eyes to track the player, but Im trying to figure out the best way to do it.

I have looked at tons of tutorials, most say, you can use UV scrolling techniques, or lift and duplicate faces and have multiple materials, one asset on the asset store simply made each expression its own material and animated them using animation clips! but Id rather avoid this.

im starting to think its not worth the fuss.

im trying to achieve effects similar to this game:

and also:

any ideas on the best Unity engine approach for this?

thank you.

 

How about using sprite sheets for the animations?