Longbox55, I checked again this morning and do have power to the switch, and from there to the connections halfway back the frame.
Here is a diagram of the relevant harness section at that point:
http://i35.photobucket.com/albums/d188/pathwayrev/1959%20Chevy%20Pickup/wiring_zpsldxoerom.jpgNote: the black of each LED is running lights and the white is ground.
The white that enters at the top of the front harness is powered when the pedal is depressed and goes through that loop...back to the front. None of that brake light power goes through any of the wires to the LED tail lights, at least that I have found. I have working running lights and still have to do the wiring for the directionals.
Before I hack into the system is there something I'm missing? Doesn't seem like they'd screw up the harness but I can't make sense of it.