If you are talking about a "68" mustang,,the parking /turn signal lights are the small lights in the valance directly below the headlights. if you have lights in the grill they should be fog or driving lights,,,could be something after market also,,hard to tell with out pictures,,,
If by front valance you mean the lower front of the car, then yes, they serve both as "fog" lights so to speak, as well as blinkers. If you have lights in the grille itself those are strictly brighter fog lamps. If those blink lights are not working, it could be a couple of things. When I got my 68, the rheostat in the headlight switch was bad, and the switch was worn so nothing but the headlights worked. In order to have those blinker-fog lamps working check the headlight switch, wiring from the harness to the fixture itself, and of course, the bulbs.
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