what aperture did you use and how long did you hold the shutter open?
ignoring the little details aforementioned, the most noticeable problem for me is that the oncoming headlights are more intense than the passing tails, causing your red streaks to be washed out and overexposed. that can be fixed by either going higher, as mentioned, or if that isn't possible, reduce your aperture. whenever I take these kinds of pictures, I get around f/22 aperture and at least 4-6 seconds shutter speed in ISO400.