It turns out that the multi-function switch does power the brake lights. The entire circuit receives power thru fuse 6 (40 amp) in the PDC. Fuse 20 (20 amp) powers the stop lamp switch. That wire is PK/DB. From the stop lamp switch (brake switch) a WT/TN wire sends power to the center brake light and the multifunction switch. From there a BR/PK wire powers the rt side and a DG/RD the left. If both fuses are good there is a continuity check you can perform on the multifunction switch.
Since neither side works or the brake lights I am inclined to believe that all you need is a fuse. If the fuse blows you have a dead short, sometimes caused by a failed bulb. If the fuse does blow, remove all four corner bulbs and the center brake light bulbs and try again.
edit; After a little more reading I'm back to the multifunction switch. Fuse 3 in the PDC powers the turn signals and fuse C powers the hazard flashers. The only common link to turn, hazard and brake is the multifunction switch. Does the center brake light work? It is the only one that does not got thru the MS.
... . thought I said that?... :-laf I've had a few '96 and '97 trucks, too. Removing the flasher module and turning on the flashers kills the brake lights and turn signals on those years, too. The cab light still works, though, same as if a fuse is blown.Again, before you go chasing ghosts in the multi-function switch, check the Hazard/flasher switch. Being on top of the steering column, they tend to fill up with dirt and water; anything spilled on the steering column goes straight for it..... Dr Pepper bing the worst I've ever seen..... looks like tar after a few days!!
I'm pretty sure that what you are calling the hazard/flasher switch IS the multifunction switch. The multi-function switch operates the turn signals, emer flashers, wipers, and windshield washer. However, now that you have pointed out that a missing module for the emergency flashers, coupled with the emer flasher switch engaged disables both the brake lights and the turn signals opens up other possibilities. If the emer flasher module is toast (or missing), and the switch is unknowingly engaged you may have come up with the answer.