This is interesting. I am very similar in this way. I have trouble looking the people that I am not super close to in the eye and, if I do, it feels very forced and I have to keep remembering to do it; however, I can look my Mommy in the eyes forever and I long to memorize the greenness and the swirls of her eyes. When I talk to Mommy, often I will look at her face as her face is very calming, even though sometimes, when I ramble, I will look off, but I do not struggle with acceptable rates of eye contact with my Mommy or with my boyfriends in the past-- in fact, I would write very frequently about the color of my many boyfriends' eyes; however, when I do not know someone that well or if I feel anxious around them, I will look them in the eyes less frequently or will focus on their lips or the place between their eyes or look in their direction, but slightly off. One teacher in junior high, I remember looking at his moustache instead of his eyes.
However, I could look at my special people's eyes forever. Also, I love looking into animal's eyes. I love this very much, having staring games with animals. Also, I usually win at staring games with humans, which is interesting... When it is just staring at someone's eyes and not doing anything else, it is anxiety inducing, but I usually just zone out and I can stare for a long time until I forget what I am doing and then blink...
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"All by myself I am a huge camellia
glowing and coming and going, flush on flush."
-Sylvia Plath, Fever 103