I used to have quite a problem with eye contact, but have pretty much come to terms with it. I am out in the (business) world too much not to have it in my arsenal. Doesn't mean I'm totally comfortable with it, but I can do it now without much discomfort.
For me, as for a lot of INFJ's I think, I didn't want to let someone inside too much. And I really didn't need to be inside them all that much either. And if I wanted to be, or needed to be, I didn't need "The Look" to do it.
I've also found that staring at a point right around their eyes, but not directly at them (like their forehead or nose) works. The other person normally can't tell.
For me, I usually just put a mask over them (my eyes) most of the time now. It's only really hard if I'm feeling strong emotion.