I'll usually close my eyes and nod along to what they're saying.
Which, I think, makes it look like I’m looking at their chest because the women I talk to almost invariably adjust their shirt in a way that suggests they’ve become uncomfortable (because they think I’m looking at their chest)
Looking intensely at someone's lips is at times the prelude to a kiss. I think this ambiguity makes them uncomfortable.
EDIT: typo
My another strategy is to make occasional eye contact while blurring my vision. To them, I'm making eye contact, whereas for me, it's not that different when I'm looking at the corner.
If you think people can't tell the difference you're gravely mistaken. I also have issues with this sort of thing, but it just requires additional work on my part. Assuming your conversation partner can't read is almost invariably a mistake.
I've had many-a-day playing some relaxing/intense video games, all the while having very in-depth conversations with both people online (no eye contact there) as well as with people in the same room who were also playing video games.
People that think you are not paying attention just need to both learn and understand that not everybody is the same in how brain functions work; we are also taught to take notes in lectures as well, and as far as I recall, there was no staring the lecturer in the eyes while I was writing shit down... (and then mulling over data and questioning as needed)
There are some people though, who are clearly very socially apt who almost stare at you while they keep talking, which actually seems weird to me. Firstly, what are they looking at? It seems kind of shameless to say it crassly. Secondly, they don't gesticulate with their eyes, which makes them harder to read.
The entire idea that someone has a problem with "holding eye contact" is misguided in my opinion. It doesn't explain what you could do to fix it, and focusing on where you are looking is most certainly going to make it worse because your visual attention is a low-level function that is supposed to work unconsciously. What one might have a problem with is not caring about the person you're talking to, or whether you catch some vague implication, or that they understand exactly where you're coming from. And if that's the problem, it's at least possible to work out some kind of solution for oneself.
I've overcome this to a degree with a lot of practise, but it's not my comfort zone.