When you are troubleshooting electrical issues, the general approach is to start at the battery and work your way down to the device, checking for voltage at every step along the way. The problem is going to be somewhere between where you see the voltage and where you don't.
I don't have a schematic handy for your truck, but you can get them from Rock Auto. On the schematic, start at the headlights and trace your way back to the battery. Then, on the truck, start at the battery and check for voltage along that same path you traced on the schematic. Where you lose the voltage you find your problem. Check the wires going into each switch, then check the wires going out. Does the switch toggle the voltage?
From other's answers on here, it sounds as if your path is going to be battery to headlight switch, headlight switch to multi-function switch, multi-function switch to headlights.