You can if you rewire the lights between the lights and the switch. Otherwise, I don't think anyone has figured it out that I know of. There was someone here who used the factory wiring to put in his own after market fog lights. He mentioned something about leaving out the relay and the fog lights are always on, or are on when the parking lights are on. I'll have to search through a few threads to find that one.
This thread shows the wiring schematic for the fog lights. According to this, the fog lights should be coming on when the tail lights are on. But that is not the case. Maybe it can be rewired at junction A38, if we can find out where that is.
http://www.toyotatundraforum.com/ele...g-diagram.html