I have to agree with the closed eyes OK faction. Since I sing a lot of old ballads, many of which tell sad stories, though I'm not always aware of it I'm sure I close my eyes a lot...the songs are very moving and I am inside them if I'm to do them right.

I've been to many professional concerts, given by musicians with very easy, accessible delivery, no nerves. But often these musicians sing with their eyes closed, maybe not thru an entire song, but certainly at intense parts. Which seems perfectly natural to me...sometimes if I'm really into it I listen with closed eyes as well. Can't imagine feeling nervous or ignored...if the performer is doing a moving song well I'm being carried along no matter what, and the sharing of that great experience is thru the ears, not the eyes.