I don't know a ton about the Fortune II, but generally speaking door optics work in pairs, one sender (emitter) and one receiver. Only the sender/emitter will appear to light up when viewed through a video viewfinder (digital camera, phone, etc.) -- the receiver will not.
You are correct about the machine not playing due to the door open condition. The "Closure" and "Restart" messages are rather benign, although it's unusual to have both a "closure" and a "door open" message appear at the same time -- that's contradictory, as the "closure" message is supposed to indicate that the door was open, is now closed, and a paid game has not yet been played. "Restart", for the record, just indicates that the machine had been powered down and is now back on, and a paid game has not yet been played.