But you're like me and can't think of a great place for a stand and haven't bothered with buying one, this might work for you. Takes about 30 seconds, won't harm the brush or anything else and works great.

A disc of velcro solves the problem for me. I put the nappy side on the top of the brush where I used to stand it and I put the nylon-hook side under the bottom of the towel rack. Now it's out of the way from everyone else and super easy to get and put back.