Air carrier Captain reported a taxiway incursion at DCA after being unable to see the taxiway centerline at night due to poor markings and a buildup of rubber on the runway.

Narrative

Flight delayed due to ground stop at ZZZ for storms in New York Area. We were parked in the hold bay for Runway 15. Once the ground stop lifted we had a maintenance issue that required a MEL. While waiting for the amended release; the wind picked up at DCA. Due to the winds we were unable to accept Runway 15. We followed the runway change items and set up for a Runway 19 departure. Our taxi instructions were to exit the hold bay; taxi on Runway 15; turn left on K and hold short Runway 19. We accepted the taxi instructions. I briefed to the First Officer (FO) that it will be difficult to see taxiway K at night as it is a sharp left turn from Runway 15. We taxied at a slow pace; both heads up. I had the NAV; beacon; strobes; logo; wing inspection; taxi and nose landing lights on. We had just passed the turn for K when ground informed us that we had missed the turn. Neither one of us saw it. We were instructed to hold position; then we were instructed to turn left on taxiway J and hold short Runway 19. We complied with the instructions. There were no traffic conflicts throughout our taxi.At night it is very difficult to spot taxiway K when heading south on Runway 15. A better instruction would have been to turn left on taxiway S. We could have asked for the left turn at S. There was no traffic in the area that would impede us. Turning on the wing landing lights may have helped; however I felt like we had sufficient illumination. The angle of the blue taxi lights make it hard to judge where the taxiway is. There is a buildup of rubber on the runway in that area so the taxi center-line is obscured.