It is there to let you know something is wrong with the brake lamp, either a burnt out light bulb or loose connection or corroded recepticle.

 

Yep I switched to led brake lights too and mine stays on. Pretty annoying. It thinks the bulb is out since leds have like no resistance. Somewhere there is a thread out there on how to bypass that light. And I'm pretty sure cruise control won't work with that light on.

 

Running the spoiler instead of the interior 3rd brake light will cause it for sure. I found that out when I added a spoiler to one of my 3rd gens. It also happens when you go the opposite direction, and remove the spoiler. My current 3rd gen had a factory installed spoiler so there is no interior 3rd brake light. I took care of that light by disassembling the gauge cluster and putting a small piece of tape over the LED. I no longer have the light on but I also don't have an indicator to tell me when a bulb goes out lol.