Intrigued by this idea. My parking brake has been disconnected since I changed the batteries six months ago. I've become quite adept at parking in such a way that the buggy doesn't roll anywhere, although there have been a couple of times I've done that and one of the cows has started using it as a scratching post and sent it off down the hill!
R, next time it stops get out and see if the brake lights are on. The brake lights will shut off the motor and the brake light switch is problematic. May not be your problem, but is worth looking at.