Mark.... I'm an 'old school' car owner but I'm presuming that even in the modern car world the fog light doesn't go through the ecu or half a dozen computers... There's only a finite number of things that will make it not work... Rigging in a complete parallel circuit seems a bit drastic (unless, say, there's a wire break somewhere in a wrapped loom and it's going to be easier to run a new wire than dig it out).... With a meter or test lamp you should be able to chase power into the switch, out of the switch, other end of the wire to the light and into the bulb holder..... If you think the switch is dodgy the first two should confirm.
K