How to make eyes that stare at a player's mouse position?

Either make a gui with 2 black dots that move to the intersection point of the gui's surface and a line between the object and a point just left and right of the characters' heads position (so inside the head), or make 2 objects like flat cylinders and do the same approach.

If the intersection falls of the gui surface that means you have to turn your head, so then either max the position of the eyes at the border or set their transparency to one (or turn the head).

So far I like my own animations that turn the characters head over y-axis, rather than the eyes, it's also easier, but both are possible.