If you really need a fog light, you should be using it without the headlights. The whole point of a fog light is to not reflect back from the fog (as much), so having the headlights on defeats the purpose.
And unless you have a pretty beefy alternator, I don't think you would want it on all the time you have the headlights on. The stock generator will keep up, just barely, but only at higher rpm. Trying to run an extra light in town or worse yet a big traffic jam, is a recipe for a dead battery.
So my suggestion would be to use a separate switch, but feed it (or the relay) from the running light switch, so you can't forget to turn on the tail lights when running the fog light. Then you can still show off your fog light when there's no fog, but get the right configuration if you should happen to need it for fog.