I had learned about eye contact from public speaking long before I started singing, so it wasn't a big deal. When I first started speaking, I had to concentrate on making eye contact with people in various locations in the audience. After a while, it became natural. I think concentrating on doing it simply got me to a point where I wasn't afraid to do something that was natural.

I believe we're afraid of looking people in the eye because we might see disapproval. I've never seen that, even when I'm not doing such a good job. When folks see that they're noticed, they look back at you with encouragement, or they look somewhere else. Often, the support I can feel during a song is more important and rewarding than any applause afterwards.

As an audience member, I have to say I don't mind if a singer sings with their eyes closed. I usually don't even notice they aren't looking at the audience, and I figure they're just "getting into" the song. The pros I've seen do this DO look at folks (or seem to) when they talk in between the songs, though.

Folks in any audience are looking for reasons to enjoy your music. They are NOT looking for reasons to be miserable. Start off looking at just a couple of happy people before you sing, and smile at them. Invite them to join you in a conspiracy of song, and I bet they'll smile back.