When I played Legion baseball I switch hit. Line drive righty; contact hitter lefty. Natural right batter, but better BA by 50-75 from the left. Stranger was that I stood more "open" righty than lefty. (I was semi-closed lefty.) That's messed up because "should be" says contact hitters (me left) normally stand open and power righties normally stand closed at the plate.
My then optometrist was at game one day and explained what I didn't realize: I am hugely right eye dominant and my body was adjusting to get that right eye to where it could see best. In this case seeing the ball was more important than which hand was where on the bat when it came to batting average.
All this, this whole draw circles, open jars, swing sticks, conversation just lends to one of my theorems of life: Humans are strange critters.