Is it possible you bought a knockoff flasher module?
Virtually all "aftermarket" HMMWV electronic parts are crap, unless you bought it from a reputable dealer, Kascar, HPG, MAC Motors or AMG you very likely bought crap.
I would have to study the schematics again but I do not believe the turn signal flasher has anything to do with the brake lights.
The above statement also goes for the turn signal switch, tons of knockoffs out there.
EDIT, the flasher has nothing to do with the brake lights, when the turn signal switch is in the neutral position the turn signal flasher is completely out of the circuit.