Mrs. Lemon, I sing with my eyes closed a lot, and have no problem whatsoever watching someone else do the same. If the singer feels no discomfort or embarrassment, neither will the audience. And as long as what they're hearing is pleasing, what they're looking at isn't so much of an issue. Stage presence comes in many different forms.

We rarely play in settings where there is a still audience. We are frequently outdoors, with people milling about everywhichway, and it can be very distracting. If I sing with eyes open, I focus on a spot over the audience's heads.