I've always had a bit of trouble looking people in the eyes. I could never win one of those staring contests when I was a kid.
Well recently, I have accidentally stumbled upon a solution. It's nothing silly like looking at their nose or anything. If I was to be able to do that it would give me continuous problems in regards to wondering if they could tell I was actually staring at their nose. And what if they have dangly hairs? Disgusting.
Also my technique is not always conducive to having a conversation. It doesn't allow a lot of time for concentrating on what the other party is saying.
What I have come to discover is that I can look someone in the eyes indefinitely if I make up mean and vulgar descriptions of their eyes. It also helps me remember what color they were if the question should ever come up in the future. Example:
As the eye contact is forced to continue, the focus starts going to the flaws: What are those two dots on the right side? Are they little bits of fermented fecal splash damage?
It creates huge amounts of entertainment. When you start giggling at your internalized descriptive verbiage and the person with the gruesome eyes asks what you are laughing about just tell them you told yourself a joke and it was funny. I recommend having a random joke handy.