Hi Bullet

I only use the rule of thirds as a guideline, as Jay says you'd probably do some tweaks when you put the eyes in the head, depending on lighting/type of character ( meaning having a concave or a convex iris).
I see you have used a Polysphere as the eyeball, try doing it using a nurbs sphere and by inserting isoparms and scaling and moving points adjust the shape, nurbs give a more natural fall of imo.
The reason it doesn't look right could be the fact that you're in an orthographic view which tends to distort, try doing a 3/4 render in the perspective view and use IPR to tweak it.
try adding reflection and refraction (blur) and add a HDRI Image as a lightsource( maybe only for the reflections).

And no Jay I haven't stopped with Snape, I have some issues with my bladder which all of a sudden seemed to play up another thing is that I have been watching a couple of tutorials on charactermodeling, which I think are worth sharing here:
https://eat3d.com/maya_portraits
https://www.thegnomonworkshop.com/sto...kles-in-ZBrush
https://www.thegnomonworkshop.com/sto...acter-Modeling
And yet another thing is trying to get my head around renderman, it's a really great render( or better said shading) engine, but there is surprising little info on it, you either have something super simplistic , or something very complex ( an ILM paper on subsurface scattering algorithyms).
If anyone here is interested in giving renderman a go, they have made their courseware public :
https://renderman.pixar.com/coursewa...w/Main/WebHome
You can ask them to give an eval license, in general they aren't very difficult( which is surprising since they are a big company) and let you try it out and try to think with you as well.
Sorry for hogging your thread Bullit