Reasons to watch Hendrix at WWoodstock concert number 4023: when he just seems to be the music, and it comes out through his guitar. He doesn't need to see the neck with his eyes, he knows it like his own body, like his own mind.
I sometimes close my eyes while playing, but I tend to keep them open while I am singing. I always am tempted to close my eyes, but I often find that audiences connect well with bands that are speaking directly to them. I try to make eye contact sometimes, though it is harder on the nerves, it makes the performance more intimate and personal, less staged.