Where the kata came from, what it "meant" I cannot know. All I can do with certainty is explore the kata as I understand it currently. If I understand the what & why's of how we demonstrate it... I am far, far ahead of the game.
Why it might be called 13...how can we possibly know? And once "knowing", what fundamental value will that hold? Some strangely contend "13" refers to the number of breaths done during the kata. (in & out =2) Others actually maintain there are 13 opponents defeated. Some propose it is a philosphic designation (ie Buddhist/Taoist) whereby that number has unknown serious importance.
Whatever we believe... will that knowledge help deciper the movements, subtlities, nuances? If not, it is a curiousity but not especially helpful I fear... I wish I had the definative answer for you, but the question leads to madness