Did you put in a Digitrax decoder in your S1, like the one that Randy used in his handy pictoral? I put a Lenz LE0512 “Micro” (N-scale) decoder in mine and haven’t had any problems with it. I also bypassed the socket and soldered the wires right to the decoder.
Try turning the decoder plug around. Normally, if you plug one in backwards the train will run in the opposite direction, but should still run in both directions. Having the decoder plugged in backwards in some engines will cause lighting problems.