Pin A: Stop Lamp Switch. Runs through brake light switch to Pin K.
Pin K: Stop Lamp Switch. Runs from pin A through brake light switch.
Pin C: Stop Lights. Hot when brakes applied. Runs to turn signal switch if used.
In my experience the brake light switch makes contact (closed circuit / continuity) when you step on the pedal, allowing current to flow to the lights and turn them on. I would guess that A and K just get tied together (continuity, as if the pedal was being stepped on to allow current to flow) that being said, you should probably stick a 7.5 or 5 amp fuse on that wire just to make sure nothing gets too hot when you test it.
Just a guess, but the circuit (from positive to "load" or ground) goes from A to the nonexistant brake switch (or wires tied together) back to K and then comes out of the switch again on pin C (+ voltage to brake lights) which doesn't make sense to me because if they want the ability to kill the lights it could just go from A to the switch to the lights and they could kill it before it even leaves your fancy switch.
I'd really need to see what the switch's internal circuit diagram looks like to say anything for sure (or spend some quality time with an ohm-meter). If you can find a link to the Humvee wiring diagram, that might help - it would also tell me it the switch controls everything on the ground side or by supplying voltage (big diff)
One other oddity, from the pinout you posted, where does it get power from?