Here is a FWIW:
On cars where I've installed aftermarket fog and or driving lights, I've used headlight relays and SPDT (single pole, double throw) switches.
The switches are basically ON-OFF-ON switches. To power the switch, I've Tee'd off of the high beams for one throw and an "ignition on" power source for the other. That way I can power the fog or driving lights to be on when the High beams are on (filler light on back roads) or to be on when the car was running (when I wanted them to be on. I have been in fog and snow conditions when the low beams were too much light)(yah, I know, this wasn't legal, but no one else was on the roads. It was that bad. Just one of the joys of having to go to work when nobody else was allowed on the roads).
John