Rear running lights

Can't turn my rear lights off

My wife's 2013 Elantra GT has a very similar issue where the left-side front/back running lights and the license plate light are not properly working since May 2019. The issue is the left side running lights/markers lights and the license plate light come on like they should for half a second and then immediately turn off. The right side works fine. All other light functions work: turn signals, brake lights, backup lights and emergency lights. The funnest thing is that the left side running lights and license plate light are on when the brake is pressed. When the brake pedal is released, those lights are off again. I have checked almost all fuses inside the engine and inside the cabin and all the bulbs with multimeter, everything is at working condition. The car has no accident and all recalls, including recent recall for brake pedal was serviced in October 2018. The dealer wanted to charge 2 hours labor to perform the electrical circuit diagnostics, so any help is appreciated here!