Eye Contact

Here’s an idea: Sunglasses. Of course you can’t wear them inside without looking silly, but outside they can give you some freedom. My strategy is I looks around the way the other person does. I imitate them. Say they look into my eyes for 20 seconds, at a stack of paper for thirty, and then at a wall for ten. I watch their general face or body movement while they do this (as well as note what they are looking at. They might refer to it) then when they look back at me look into their eyes for roughly the same amount of time they looked into mine then look around for roughly the same amount of time (though a different objects) and repeat.
If you want to try that you could take sunglasses a step further and practice with them on. That way when you get tired you can just avoid eye contact!

Personally, I don’t think I’ve ever had problem with eye contact. I’ve always been shy. I just have problems trying to make small talk and thinking of things to say.