I'm left handed, sort of. So many things I do are equally well left or right.
The Zubat is strapped to my right calf. If I had a light saber, I'd clip it there. Draws and stows with either hand.
I'm having to pull the chainsaw from the right side, which I find inconvenient at times. I have found stowing and tending it from either side to be equally [in]convenient. I wonder if this alternating sides is being gentler on my body, and maybe physiologically a close second to tethering it in the rear.