I have a 88 F-350 7.3L Deisel with a parking light problem. When I pull the **** out to turn on the parking lights, nothing happens. If I pull it between the click of the parking light and headlights, they will come on. But when I pull the **** all the way out, I get the headlights without parking lights. I can't have both the parking lights and headlights on at the same time.

I have replaced the switch with a brand new one with no change. All my fuses are good. What could the problem be.

Thanks in advance.