Retread,
Good question. If you powered the light AFTER the brake light switch, but BEFORE and turn signal switching, it seems you could do without the logic circuit.
My bet is that the logic circuit was designed for new rigs where you couldn't access the brake circuit as easily before it gets confused in the turn signal spaghetti.
What would happen if you dumped the logic circuit, grounded the light and powered it from the switched side of the brake switch...it should light up on every brake application it seems to me!
Stuart