I was browsing YouTube in the recent past, and was watching a video with an autism theme. I read the comments. People were talking about their attempts at making eye contact, and stuff about that.
Disclaimer: I'm not diagnosed with autism, but I've never been medically evaluated for it, either, and I do have a number of traits that are common in autism. I don't have self-diagnosed autism, but I acknowledge that I could possibly be on the spectrum. I do not consider my neurology to be like that of other people I know (I feel like a new species of human or something--and not a less advanced one). I do like people with autism, though, and I find them interesting. I differ from stereotypically autistic people in a number of ways. Instead of being super literal, I tend to be metaphorical (but I'm more literal than your average person about lots of things, although I'm less literal than them at the same time); I understand and can read general emotions fine (but I know enough to realize emotional intelligence isn't something you just have or don't have; it's something you can continue to improve on, IMO; you don't have to have autism to get better at it). One trait I share with autistic individuals is that I don't like to make eye contact (at least, not with alpha types, super popular people, vociferous emotional people, people who are not satisfied with me, when there's drama, when I don't want to be [incorrectly] psychoanalyzed, when I'm bored, when my working memory is repeatedly exhausted by listening, when it's too bright, when I'm nervous, etc.)
Anyway, I thought about my own awkward experiences trying to make eye contact with people where I wasn't sure if I was looking at them too much (or where I was sure I was looking too much), or if they thought I was looking away too much, or if they sensed how I was feeling, or whatever. Someone in the comments (of the YouTube video) mentioned finding a balance. I decided finding a balance wasn't key. It's still awkward even with the right balance. The problem is, you're (figurative you--not actually you) doing it manually, and it's nerve-wrecking. It's hard to focus on what the people are actually saying when you're looking them in the eye.
So, later, I realized something. It's not about how much you look at them. It's about how you listen. I was listening with my ears/brain, but in situations where it seems awkward, I think what needs to be done is to listen emotionally, or with the heart. You'll note that it's not equally difficult with every person. Autistic people are great, because they don't care if you look at them a terrible lot. It can be more difficult with the people who really want or need the eye contact the most. I think what those people want isn't simply a mental communication pathway, but they speak with their emotions, and it's better if you receive their communication with emotions.
So, rather than stare at them with a deadpan face, listening, and being full of nerves, try to feel love for them as they speak. Try to feel their words, expressions, and body language (instead of thinking/comprehending it). Try to love them. You may find it easier to have automatic eye contact. If you listen with your emotions/heart, you may find that you actually want to look at them.
It should be noted that listening with concern is not the same thing as listening with your heart. The fact that you're listening at all shows that you have concern. Of course, you're probably trying full throttle to be concerned. Don't just try to understand or empathize. Try to listen with your emotions/feelings instead of (not in addition to) your ears (but don't turn your ears off).
Anyway, I don't know that this tip would work for someone with autism, but it worked for me the one time I tried it! :) I'll have to remember to do it more.
Of course, feelings of love aren't necessarily easy to just poof out of nowhere (especially if you happen to have emotional blunting or something), but it does get easier as you cultivate and practice, and improve your physiology (e.g. with nutrition and supplements). It helps if you observe love (and positive emotions), often (yes, TV/movies work).
You might be surprised that I mentioned nutrition and supplements. They're important for things like circulation, brain health, neurotransmitters, hormonal balance, antioxidants, toxin-handling/removal, etc. Those things can impact emotions.
I recommend staying attuned to your sensitivity. Don't do things that desensitize your emotions (e.g. such as consuming media with mature content, playing games where you kill stuff, swatting flies, using sarcasm, exaggerating, using foul language, being irreverent, making fun of stuff, watching too many parodies, name-calling, even if you're not talking about a person, pigeon-holing, judging, etc.) As you become more sensitive (in good ways), you're probably more likely to increase in emotional intelligence, compassion, and other such.
You know, I've discovered that flies are about as easy to catch as they are to swat. Just catch them and put them outside. It works, and it feels a lot better, emotionally (the trick to catching them is moving slowly/gradually). Talk to plants. Say, 'Thank you' to Alexa (don't insult her, or anyone else). Express gratitude. Pray. Let yourself cry when you cut onions. Smell some roses. Care about seemingly preposterous things that people say that matter to them (don't care too much, though, or you might upset them).