I have trouble with eye contact while I'm actually talking to someone. It's not so much that it makes me uncomfortable, it's just distracting, and I can't focus on what I want to say. I have to look away in order to find the words. I think it might depend on the subject matter, but if it involves having to imagine or consider a problem, then I have to look off to the left in order to find the words to say. I try to remember to look at their eyes as soon as I'm almost done with my sentence, though, when I don't need to be finding words anymore. My mother is exactly the same way. Both of us are kind of close to being AS, but probably not enough to go seeking a diagnosis.
I'm not particularly affectionate. I can feel very deep love for someone, but I don't express it much. I love my husband dearly, but I don't like looking in his eyes for a long time. He had lovely eyes, and I'm comfortable with him, but the long gazes bug me. That is, unless we are both being very playful, like putting our noses together and looking into each other's eyes like that. Then it's kind of fun, if I'm in that kind of mood.
One problem I've always had is that I'm often not sure how to know when a show of affection might be considered sexual or not. I have misread cues before, and accidentally sent the wrong ones. If I have no sexual interest towards the person, but I feel like I want to express affection, I end up feeling uneasy, because I'm afraid of sending the wrong signal. I also found that if you come out and say, "Could you please tell me if you meant that in a sexual way or a non-sexual way, because I can't always tell, and I don't want to misunderstand you, " it makes people so uneasy that they go away and you never see them again.
Years ago, I took a class where one of our first in-class exercises was to pair up with a same-sex classmate and look into each other's eyes for a full minute. Then we all discussed how that made us feel. It was something about personal boundaries. I had no trouble looking into my partner's eyes at all, because it was a class experiment. That made it okay. I still remember her face, 15 years later. She had trouble, though, and kept giggling. There was a young married couple in the class, and they were allowed to pair up together. They were not able to look into each other's eyes at all.