"I'm afraid that if I close my eyes everyone will silently sneak off, and I'll open my eyes at the end of the song to find an empty room." Vin Garbutt says that happened to him one time out in Malaysia or somewhere - they'd all gone off to the bar. Mind you, he very likely made it up for the story.

Closing the eyes in a serious song just seems more natural to me. More respectful even. If I'm playing an instrument I'm more likely to keep the eyes open, but I'll avoid fixing anybody with the eyes, glance around and look over the heads. But for normal singing, and unaccompanied is what I means by normal, I imagine in more likely to have the eyes shut, unless maybe it's a funny one.

Being nervous would be more likely to make me open my eyes.

I suspect there might be a cultural difference here between folkies on both sides of the Atlantic, with Americans maybe more likely to see the closed eyes as being artificial and as opening the singer to the suspicion of being a bit of a poseur; and the same maybe applies to people who prefer to sing unaccompanied. Over in English-speaking Europe eyes closed an unaccompanied seems pretty natural (among the kind of people who listen to or sing folk songs, that is.)