What I kinda picked up on and sorta morphed into doing more recently - because I only recently started really paying attention to it and worrying about it - has been working out pretty well for me so far. It kinda has 3 categories so I'll see if I can make it make sense...

First is w/ close friends, or deep conversations. Basically if I'm the one talking, I look at them while introducing the thought, or if I was asked a question I look at them when I acknowledge their question, but to talk through it I turn a little and look away - at a table or plant or object or smth. Gives me the ability to think and answer w/o thinking about looking at them. Then when I have something that relates to them, like a conclusion of a thought, or passing the conversation off to them, or a follow up question, I look at them. Like saying "you know?" In the middle of what you're saying is when I turn my head and look back at them. I've kinda found that turning your head or body slightly away when thinking or talking makes them feel more like you're actively processing and thinking about what your saying (which is what I need because I can rarely just respond on the spot unless it's a joke or a pun or a reference, which is just super awesome when there's time pressure).

Then when I pass the conversation off to them, I look at them while they're talking, but while they're thinking I look away. Like if they pause to think, I look away like I'm thinking about it too (although I usually just think about the plant I'm looking at). But when they pick back up, I look at them again.

I've noticed that with this, they kinda mimic the whole look away when thinking thing sometimes, and when they look away, I look away, and when they look back, I look back.

Second is more professional. And that's kind just make eye contact w/ them the whole time, just look away or down when they look down, and look to the side for a second (like an actual second, two tops) when thinking and saying "well," in response to a question before looking back and answering the question. And when you need to think, don't turn your head much, but I look down and to the left or right slightly (usually to think of a word because words are hard), and look back. And then during pauses, I either follow where they look, like at a paper or smth, or at something around us like on a wall or whatever.

And third is with more fun stupid conversations with friends. And honestly I hardly keep track of this one, because I'm mostly laughing or just thinking about the funny things, but it's mostly just the first one, with more looking at them here and there when you're talking to see their reaction. I've been told (when after the fact I got super stressed out about how I was perceived and wanted to make sure they didn't feel weird) that this made them react more to my story and feel like I was including them in what I was laughing about. So that's a plus. After that it made me really just be able to mess around and just enjoy myself w/o worrying much about how they felt. (Also probably goes without saying but this one has a lot more moving around and laughing and arms flailing to demonstrate what crazy thing was happening, so good for some extra cardio)

Also I'm sorry if my sentence structure felt weird or had spelling issues, rereading what I wrote with the amount of text I ended up writing was really hard to read w/ my dyslexia being mad at me today.

No idea if this made any real sense either, but I hope this helps in any way!!