A gobble is apparently an intense undertaking for a turkey. It wouldn't surprise me to find out that they close their eyes during a gobble. Have you ever tried to keep your eyes open when you sneeze? You can't. Its just a biological response. It helps to protect the eyes. Probably the same type thing with a gobble. Interesting observation, though.

btw, I wouldn't thing that a gobble would be a long enough duration to get away with much movement, anyway. Also, I doubt that their eyes are closed during the entire time, much like our sneeze. I'd like to know more-- if you find out anything, please post it.