Open your mind up a little and experiment, there are hundreds of different ways you can do this. The bust could be of Bart Simpson rolling his eyes and burping, Elvis Presley smirking, Barack Obama yapping, or Daffy Duck nodding his head and looking side to side. Whatever.
I mentioned edge loops but all you have to do is make it so that the mesh serves its function as you need it to. We're voting on how it looks in the end so who cares if you cheat a little with the mesh if the deformations look fine?
And Kreator, clay/stone renders don't require ART. Which makes for just a night's worth of rendering at the most for most setups, if that. Clay/stone renders also don't require tons of details. An eyeball could just be a sphere with a dent in it. That's how the picture above looks like, right?
There are a lot of easy characters you can work with, Pincho. Also, morphing is actually a little easier than skeletal animation when it comes to getting what you want. Use bones for the eyes, head/neck, then use morphs for the lips and eyelids/brows. If you're afraid of morphs, then just use bones for the eyes and head/neck, and even the jaw and that's all! You only have to animate two parts of the head.