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I've seen where the switch has been modified to bring on the low beams when using the high beams by modifying it internally. I'm not certain if it would work for the fogs like that with it in parking light mode. What you can do is pick up a 30 amp relay and holder/harness and wire the fogs to be on with the headlights off. I use the parking light on hot wire not the turn signal hot to energize the relays so they are on all the time. The relays get their power directly from the battery so they are brighter than normal. I was changing my stock 02 F-150 head lights out for a european style. The head lights also have relays powering them and they are bright.
Found the answer on F150 online. Remove light switch from dash with small screw driver. Using 3m jumper connector. Connect the (white/black) wire to the (brown) wire. You also have to modify the light switch. There is a arm attached to light switch stem. Turn light switch to parking lights the arm will hit the guide and not let switch pull out. Take a small file to guide and file down guide enough to pull switch out as far as the light switch does in the head light position. Then mod should work. It takes longer to write mod than do mod.