fog lights

It is standard practice that for lights only can be turned on with the dim headlights on. Almost all factory units are so wired. Mine only come on in my 97 when the headlights are on and in the dim mode. If I switch to park (the first position you describe) or turn on the brights they go out. When I install driving lights which go on with the brights, I found the fog light power switch attached to the dim side wire from the dim/bright switch in the steering column. Thus they can only com on with the dim portion of the head lights.
Ron