Colin, on mine to stop the engine the centre threaded stud/brass nut at the centre of the mag's end cap (which could be the small button you mention?) needed to be earthed. To do this without running a wire up to a handlebar switch I mounted a simple on/off switch on the back face of the tool box. There, it's out of sight, giving a modicum of security from being nicked, only a short wire was needed to reach the mag and it's handy to operate on and off.
There should be a spring loaded carbon brush inside the end cover.