I suspect that you meant that the other way around, that using same color LEDs as the lens gives optimal brightness as mentioned here:
'97 third brake light conversion to LED
However a little bit brighter white LEDs can offset that fine. Utmost efficiency isn't important for this application and there are lots of LED choices out there. You could even run a row of 3W LEDs and have it so obnoxiously bright that it causes tailgaters to back off, so long as you don't lay on the brakes long enough that it starts to overheat, or get fancy and put a thermal cutoff on a heatsink strip they're mounted to, easy and cheap would be the mechanical type you see in coffee makers, etc.
I'd pick a low temperature, maybe around 60C. If the housing isn't making a watertight seal when finished, something weatherproof (at higher cost) might be more appropriate:
2X 10A 250V KSD301 30°C~160°C Thermostat Temperature Thermal Control Switch QW | eBay
Or a KSD9700 flat pack type if space is tight:
KSD9700 | eBay