It is illegal to tamper with vehicle lighting in my country because many beginners make the lights too dim, too bright or the wrong color.
The drawing called, "Something like this" might feed 14.4V from the alternator through the diode producing 13.7V.
Since you did not post details about the LEDs then they might have an absolute maximum voltage of 9V (to 12V) and blow up. LEDs are usually fed a limited current, not a voltage.
Warm White brake lights? Or the white Leds are behind a red lens?
But a white LED is actually a blue LED and a yellow phosphor which produces not much red light. That is why car makers use red LEDs for brake lights and rear running lights. They use PWM for dimming.[/QU
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Yes I did post the Specs for the Leds in the question....
10W 900LM High Bright LED Light Lamp Chip DC 9-12V
I am from the Automotive Proto- type side of the auto industry. quite aware of the US reg.
The mention of diodes was to get attention!
The pic of the tail light, I had room for independent rows of Led's. Thus not a problem high's / low's