Tom, a common position and routing for a rear brake on a Mixte is along the bi-laterials. That way the cable routing is less convoluted. However here is a picture of the brake routing system on one of the frames one of my small woman students made. It was not a finished product at the time of the pic but rather a proof os concept just to make sure the idea would work before bothering to make specialized pieces. it worked great.
Besides the roller, the other pieces were just things laying around. The black pieces were from a rack mount and the pieces next to the roller were rack bosses.