The switch doesn't light up, at least on mine it doesn't. There is a warning light on the far left of the dashboard.
The switch is a passive latching type so the actual button position is the same on or off.
Use of rear fog lights at night in clear condition is deemed a hazard to following vehicles so, potentially a MOT fail.
When you plug in a caravan or lighted trailer the tailgate foglights should be disabled.
I would check the tow socket wiring.