Since all diodes do is restrict current to flowing in a single direction, I'm having trouble seeing a way to use that that would allow connecting the brakes to both sides, but allow one side to flash when turn signals are in use and the brakes are applied.
It would allow the signals to work correctly when the brakes are not on, but otherwise the brake would turn on both lamps.
Either there is more to it than a couple diodes or its a less than ideal solution.