I would start by using a voltmeter and seeing if you have 12 volts at the plug when the brake is applied. If the answer is yes, then the issue is with the light itself of the connector from the light. If you do not get 12 volts, then check the ground wire to that light for a secure connection.
A forum community dedicated to Jeep Wrangler owners and enthusiasts. Come join the discussion about reviews, performance, trail riding, gear, suspension, tires, classifieds, troubleshooting, maintenance, for all JL, JT, JK, TJ, YJ, and CJ models!