Don't you also need a pair of diodes so the turn signals don't illuminate the brake light?
We're talking LED bulbs here, but I'll reference incandescent just for ease of comprehension....
No diodes needed. You're adding a new separate circuit into the turns, not sharing the existing one. (you only share the ground)
The turn bulbs are originally a "single filament" bulb and only do turn signals. 2 wires: +12v and ground.
The bulb holder will accept either a single or a double filament bulb. If you use a single you get your turns. If you use a double you still only get your turns (only 2 wires that feed one filament.)
Spidey ran a wire from his brake light to each of the direction signal holders and wired them into that 2nd filament connection, and then upgraded the single bulbs to dual filament bulbs (in this case switchback LEDs)
Here's his photo taken from the above referenced thread.
This basically made them a dual circuit bulb consisting of the turns that were already there, plus the new brake circuit.
Again, the red/amber LED allowed the turn to stay amber and the new brake part to be red. Yes, it's still showing thru the amber turn signal lens, but with a red tinge to it.
As Spidey noted the goal was to have a wider larger brake light. I did it by adding higher and lower extra lights and chose not to do this style of mod... I'm just trying to explain it for anyone who wants to do this too.