Bingo, Dr. Bill! Give that man a SEE-gar! The saying goes back to the days of outhouses (and before that, whatever bush was handy) when they had no paper and made use of leaves, corn husks, or whatever else was available. Unfortunately, there were those times when a stick was the only usable item. I first heard and used the saying as "the shit end of the stick", never knowing in my youth what the implication was until I became immersed in 19th century lifestyle history fairly recently (although the saying goes much further back). Just like "don't have a pot to piss in" was coined in reference to poorer folks who couldn't afford the luxury of a chamber pot circa early-mid 2nd Millennium.