Couple of things. if the back door is loose, the front door is loose. Water does flow down hill to the front. If you have a gasket for the light install it. Obviously the lower part of the door seal is damaged, how is the top?
I would bet on wind and hard rain came in around the seal due to loose door latches, or maybe you left a widow down a bit. Hard wind and rain will push water through any loose or bad seal.