For Fog lights, I would recommend wiring the relay so that it gets power from the Parking lights rather than the headlights. Parking lights are always on when headlights are on, but the reverse is not true.

The reason for wiring Fog lights ( NOT driving lights ! ) this way is that during severe weather like heavy snow or fog, the headlights, even on low beam, reflect back too much from the snow / fog and seriously hurt the effectiveness of the fog lights, which should be mounted as far below the driver's line of sight as practical - like under the bumper, or in the lower part of the fascia.

Having driven in conditions when snowflakes are as large as a half dollar, or in heavy fog, I always find that turning off my headlights and using the Fog lights was far superior to trying to see past the glare from the low beams. Since the tail lights and parking lights are still on, I have never been pulled over for having the Fogs on without the headlights on in over 40 years, whether on the California side of Donner Pass, or in Nevada. Sadly, the OEMs don't wire cars this way, due to DOT rules made up by some bureaucrat with no experience decades ago. Fortunately, one can always add Fog lights to a vehicle, and wire them for the best visibility themselves.