I sing a cappella stuff a lot and I almost always keep my eyes closed. I have had a lot of people say to me that although they normally would find that weird or distracting etc. that somehow it was okay when I did it. I guess a lot of it depends on what sort of performer you are. I inhabit and communicate the songs better when I close my eyes. I think using your eyes to make contact is important enough when talking or storytelling or performing comic songs. But it seems quite melodramatic to do so with a sad song.

My two cents.