'Light' has for a long time meant 'understanding'. For example, "After years of trying to solve this problem, I finally saw the light" means I grasped what the solution was. In the same way, "Shine a light!" suggests that the speaker is exasperated by someone else's failure to get the answer to some question/problem. In other words, he is asking God or nature or whatever to "illuminate" the situation so that the other guy can "see" what the solution is.
I've never heard the 'and back again' version.