Yep, you've got the right switch. There is no indicator light (illumination) on the switch, the power indicator light is the one you've found in the cluster, so that sounds right.
If the rear fogs are on whenever your lights are on, and the switch does not turn off, as you think, that is wrong. It sounds like the rear fogs are powered direct from the lighting circuit.
If you have a towbar, look to the wiring in the back 12n socket. Faulty or poorly executed towbar wiring is a
common issue with lighting/wiring problems. Rear fog light wire colour in the 12n socket should be blue, and IIRC the Toyota loom colour is a light blue or grey for the rear fog lights.
I would check in that socket first, in case someone has wired the fog light wires into the lighting circuit,as that would power them up with a direct feed when lights are on. Of course it could be the switch, so in the absence of obvious wiring faults, you may have to do testing. Good luck.