A word for "when you are looking at somebody but thinking something else"?

Is there a word for "when you are looking at somebody but thinking something else"?

Like when you stare at somebody but you are thinking of something else.

Solution 1:

It sounds to me like you’re describing the old “thousand mile stare", which usually happens to me when I am preoccupied by something weighing heavily on my mind, or when a strong or vivid memory suddenly seizes my attention.

Thousand Mile Stare

To stare blankly while deeply in thought as if you were looking a thousand miles away. Usually brought on by a stressful event or situation, causing one to block out their surroundings and stare off into nothing. See the Urban Dictionary Thousand Mile Stare

Solution 2:

It depends on the context of the sentence, and from whose point of view it is.

From the perspective of the viewer, you could say that the person was inadvertently staring at the other person, or was unawares.

The person being looked at could use the idiom he/she looked right through me.