^^This is a possibility. I
highly reccommend using fairly low wattage fog lights. As I stated above I am using 50 watt ea. bulbs. They are working great and have run flawlessly for months. The parking lights obviously draw a certain amount of current. By "piggy-backing" the fogs on the same wiring you are pulling that much more current through the same circuit. This could quickly become too much. Once that happens a fuse
should blow. If not then the wires or switch could possibly burn out. If you are using larger type fogs then do as
blckpwdr suggests and use relays.
A proper (relay) setup could use the parking lights as the trigger for the relay. Then with (fuse protected) direct battery power, you would have no problems and could run whatever size fogs you want.
The bottom line is:
This "piggy-back" method works but "try it at your own risk".