how to pass parameters to single animation

I have a character in which looks like below.

The Hero GameObject it self. Doesn't have any renderer. What i wanted to do is to make the character looks around like.

The character will look in any random direction after 1 sec. I have done these kind of things with scripts. but unity's UI is making me confused. I think it is possible using Vector3.Lerp and storing all the eyes positions in variables.

I thing guys i'm not worried about the maths involve in doing so. I'm troubled with unity's way of doing it. and also can i achieve this using Animator? without creating so much 'anim' files