The pupils in the eyes in the statues were usually made from bronze, ivory or precious stones and they have not survived the pillaging that has been going on since humans evolved. In rare cases they have survived. This is Charioteer of Delphi, also known as Heniokhos. He is one of the few Greek bronzes to still have inlaid glass eyes which are quite magnificent.
If you would like to see one of these ancient glass eyes up close please follow this link. I couldn't copy the image but it is worth looking at as it is quite remarkable as is the explanation for its creation.
Exotropic, I have learned is a form of strabismus in which one or both of the eyes deviate outward. Also called walleye. (the freedictionary.com)
But do not despair. Your artistic hero's reputation is intact. The researchers (Saad Shaikh, MD & James Leonard-Amodeo) concluded that Michelangelo had used the David’s exodeviation as an artistic tool. And I quote:
Approaching the statue from its left, the viewer notes that the left eye is staring towards (and above) him, as if focusing cunningly on the giant Goliath. However, the right eye is not fully visible from this angle because it is hidden behind the sling. If one stands to the statue’s right and circles around the right, the right eye remains visible but the left eye disappears. Michelangelo must have calculated every angle and considered the position of the viewer when carving out the eyes. The left eye accords with the direction of the body’s intended move—David would be throwing the stone toward his left and the eye, naturally, would fixate its gaze in that direction. The right eye, when combined with the rest of the body seen from the right side, accords perfectly with those qualities the commissioners of the work wanted the statue to reflect—power, cunning and intelligence. (ncbi.nlm.nih.gov)
In every block of marble I see a statue as plain as though it stood before me, shaped and perfect in attitude and action. I have only to hew away the rough walls that imprison the lovely apparition to reveal it to the other eyes as mine see it. Michelangelo (Credit: ncbi.nlm.nih.gov