hmm... level 13 is just a wacky room that said as I entered "to be continued" "for now..."
Guess.. I beat it?
"spoiler:"
Tiles... take them from the back wall, pop the bridge up, put the tiles in the slots under the bridge, line up the lines of the tiles with the lines in the sides of the slots... use the box to catch the head and put it in to the maze to hit the unlock switch for you.