Help ( mouse follower issues)

I guesse you can all what i am trying to achive an advanced mouse follower.
Have you seen the mouse follower of the eyes that follow the mouse. Well i kinda of want to achive that same effects but with just the head folowing the mouse, but i dont want the head to break, so i need to have constraints on it.

I have a deer and when you get close enough i want the head to follow the movement of the mouse but when you go outside of a area i want it to stop following, so that the head doesnt flip.

Here is a image of what i am trying to achive…i know reading it is kinda of difficult.

the biggest thing is that i dont want to head to flip (“breack”). just like a simple nod