For the UX, I was imagining you have to press a button to instruct the computer that "Hey I'd like for you to move my cursor via eye-tracking". That way the cursor only moves when you want it to (same as today w/ a mouse) and isn't constantly moving around when you look around. Press down to have it move cursor to eye-tracked position and stop when you release.
Could possibly decompose the space bar to have that space for that button. Like have 3 mouse buttons where the right side of space bar is: (a) Track my eye movement while I press down and stop when I release, (b) left-click, (c) right click. Then you don't have to leave home row on your keyboard.
Or add one of those IBM Thinkpad mouse knubs somewhere on a keyboard and use those as mouse buttons instead of a mouse itself.
Idk, easy to dream of course. Hard to execute.