I have trouble with this too. It is worst when they are feeling something strongly. Like when my husband gets home from work and gets excited or angry about his day. I just can't look him in the eye or I flinch from the intensity of the emotions coming at me. If the other person is thinking or feeling more calmly then I don't have as much problem with meeting their eye. I think that is why I prefer to chat with people through writing then with face time. I can't read into their words in writing as much as I can with their tone, body language and emotions all coming at me in person.
Welcome to EC Eddie. I hope you find the answers you are looking for.
This is the story of my life. I'd get fussed at a lot as a child because my parents thought I was just being rude by avoiding eye contact. When your a kid, you think that everyone experiences the world similarly to you so I just thought everyone felt very uncomfortable (e.i. scared and flooded with weird emotions) when looking in people's eyes, but they just powered through it for the sake of being polite.
1.) Get a job in which people expect you to be a little odd (I say that as someone in one of those jobs; people don't quite expect me to behave normally so I don't have to look everyone in the eyes all the time).
2.) Hang out with people from countries that see looking someone straight in the eyes as a sign of disrespect. They won't be bothered by a lack of eye contact.
3.) When you know you are going to be in situations in which eye contact is extremely important such as going into a business meeting at an American company, take a few minutes to focus on yourself and kind of extra shield yourself.
4.) If you aren't in situation 1,2, or 3, just look at the nose as a Robert Stewart mentioned, or do what I do and look at their mouth. People can kind of pick up on you not making eye contact, but it is close enough that it doesn't make them feel uncomfortable (This doesn't work in situation 3). Plus, this has the added benefit of letting you lip-read in case you happen to miss something someone said.