Unless I'm really anxious, I try to make eye contact with people because I know it's very important to them. I kind of figured out how long I should look into their eyes, how often look away; some topics may require longer looking-away periods like when someone's feeling guilty, some require longer eye contact and maybe a sympathetic gesture if someone's distressed or sad.
If I'm moving around or if I'm distracted (like in a shop or on the bus - so many people) I just simply forget to make eye contact and even when I speak to people I just can't remember to, even briefly, look into their eyes. It's especially hard when I'm in a queue in a supermarket, packing things into a bag, then getting a points card, credit card, entering PIN, there are folks behind me moving things out of their trolleys... it's just too much at once for me to comfortably make eye contact. My daughter recently pointed it out to me, that I speak to people sometimes without even looking at them.
I've made a massive improvement over decades. As a kid I had my eyes just glued to the ground 80% of time and I used to talk to kids (when I actually felt like it, which was rare) without looking at them most of the time. My hair covered my eyes partially too, like I was hiding behind it.
Still, if people talk to me and stare very intensely (and say "look me in the eye!") it can simply make me cry. Once I had to get off the bus because a random woman was staring and me and I started to cry and feel shaky. It took me hours to calm down.