Who knows about turn signal wiring?

In a standard setup the blinker mechanism interrupts the power to the tail light in question.

So to make one side flash and the other side stay on you have to selectively switch which side the blinker mech is connected to.

The turn signal switch does this

Your diodes prevent back feed but the continuously on brake power overrides the blinking power from the flasher mech.

In a post I drew up how A turn signal switch can accomplish the switching.

I'll look and see if I can find it.