This summer I built a system that uses slight head movements for refinement, allowing hands free mousing as fast as a trackpad. However, eye trackers good enough for the system to be pleasant cost $10000+. I have ideas that would allow it to work with a $100 eye tracker, but even then it has the downside that the computer vision for your mouse will peg one core.
(Edit update: by "detectable" I mean theoretically detectable by a really good camera and software. In other words, it seems you are arguing the tech is impossible even theoretically due to some aspect of biology. Am I following you correctly there? Thanks)
Your field of vision (and focus) is much bigger than 1 degree, so any part of the image that you are "looking at" is something the brain is doing to the image as post processing, not something your eyeball is doing.