If you use connecting rods, I would use the complete rod. Shorten the rod bolts and mount them to a board that you can mount on the wall. Then find a wood or metal dowel the size of the wrist pin hole. Two hairpins will keep the rod from sliding out. You could also do that for ******* paper if you have a bathroom in the garage.
One thing you might want to do, if you make one and do attach it to a wood board, is on the board, in the middle, attach a hinge. Then on the hinge, attach a piece of metal that would lay on top of the towel roll. This will keep the roll from unwinding on it's own. Anyone that has a roll of paper towels in the garage with the doors open and breeze blowing, knows what I mean. Don't make fun of the sketch. I can't draw.