I believer I will talk about a couple of things today. First a little more about the eyes that follow you problem. I am traveling (again) and I carry a few photos of my wife and kids in my computer bag. I remember what they look like, but women always ask me if I have photos of my family and disapprove if I don't. Men, never ask.
So, I propped one of the pictures of my kids up against the desk lamp in my motel room and walked back and forth in front if it. The eyes in the photograph seemed always to follow me. I am certain that the camera didn't manipulate the images in some special way to make that happen. Nor did the camera employ some artifice or covert mathematical operation to secure the effect. Oddly though, people never remark about the eyes in a photograph following you around, at least I have never heard that. I think that backs up M. Guilmets explanation, and as I said earlier, it requires no special manipulation to paint a portrait with eyes that "follow" you except for having the sitter train their eyes on you as you paint them.
I think that a little of what is underlying this whole thing is a popular idea or need for the artist to be a shaman or possessed of some secret knowledge. The idea that a paintings eyes follow you around because of some little known contrivance appeals enormously to that. It reinforces the idea that the painting has been imbued with some special and mysterious "life" that is slightly otherworldly.
Most people, OK, not most, but a great number of people who I meet tell me that either they, or their mother is(or was) an artist. My standard reply is to show a warm and supportive smile as I ask "Cool! Maybe I have seen your work, where are you showing?" That always seems to sort things out. When it is Moms work they will tell me about, or if possible show me a portrait Mom did of the kids. As I look at it, I can easily tell it was made by copying a photograph by someone with no particular ability or knowledge because it contains no structure or form. That is, rather than the modeling explaining the planes and surface of the heads, the shading is like dirt on the surface or has cast shadows that fall randomly across the features rather than being arranged to display the features expressively. As I observe this I usually hear the proud relative saying "and the eyes actually follow you around the room"! That being presented as the final authoritative argument for the high quality of Moms art. See, Mom can do "it". The painting also "looks just like them".
I try to be supportive and move on to admiring their collection of unicorns or something, but it makes me feel foreign. I always wish that the people that I met knew more about painting, but it is obscure to them. After spending a lifetime honing my craft, it is always a little scary when you discover that most "normal" or educated people don't know the difference.