Hmm,13.8 is a little low but good enough for bright lights. Check the voltage at the headlight lamp,engine running at a fast idle,if it's about the same as at the battery, good.You said you ran a ground, did you run it all the way back to the battery negative? Never rely on the frame and sheet metal for grounding.Check the voltage again at the headlight terminal using the new grounding conductor. After doing that,if it doesn't improve,then there's nothing wrong,huh?