I loved that scene.
There was apparently a scene cut out that explained how Indy knew to keep their eyes shut. That scene where Indy and Sallah met that old man who translated the language on the headpiece to the Staff of Ra had some dialogue removed. After he said, "this is a warning not to disturb the Ark of the Covenant," he also tells them that which is contained in the Ark is not meant for the eyes of Man, and looking upon its contents would mean death. That part got cut out and they instead switch to Indy immediately asking about the height of the staff.