I'm not good with eye contact, but I learned to fake it because I was drilled to from a young age onwards. I'm not sure that's unilaterally a good thing. (The method certainly wasn't.)
Eye contact was excruciatingly difficult and unnerving for me as a child. But because I had to do it, I learned to look for a moment, mentally record the sound that someone was making while I was looking at them, and then look away and 'review' the sound, making sense of it as language, as I looked away. That's how I still cope today. Because, I can either look at you or talk to you.
It goes unnoticed in ordinary conversation, but when I'm having to take in more information, such as in professional one-on-one talks, I'm always afraid it becomes more obvious. The amount of data I have to process in the same amount of time increases, and I can't 'record' and 'review' sound bites as leisurely (relatively speaking) as I otherwise can. So I look away more, including when I'm formulating questions or explaining something, and any eye contact that does happen is briefer.
I was thinking about this very topic today. I had a longer talk with my boss this morning and was so happy to work in a tolerant environment because, elsewhere, this same - quite pleasant - conversation quite likely would have got me blacklisted for being weird. To be fair, though, I knew I would get some leeway, so I wasn't straining for pretend-normalcy at all costs. I was thinking a lot and barely making eye contact. No blacklist here, though, just praise for asking exactly the relevant questions.
When I absolutely must fake it in high-pressure situations, such as during the discussion part after talks or in meetings, where there's no script and I'm answering a particular person, I cope by looking off to the side, just past them (past their eyes) and then looking back at their eyes briefly as much as I can manage while keeping my thought process on track. It works when I have a pretty good sense of what I'm talking about, or if I there's a script - not necessarily word for word, but a line of argument or somesuch that I'm very familiar with.
But when I really have to mull something over for a bit, I absolutely cannot handle eye contact. I usually announce that I have to think about it for a moment, look away and, if at all possible, someone else takes over. That way, people can sometimes even get the idea that I'm taking them extremely seriously, which they obviously like, and it can inadvertently work in one's favour.
On balance, I cope okay, but I get annoyed that I have to put in so much work, and that that work goes completely unnoticed when I'm especially good at it. And I sometimes think how much more eloquent I could sometimes be if I didn't have to bother with the 'noise' at the same time, in situations in which strictly only content should matter.