I would certainly fight. I am pretty sure MUTCD says that as long as you crossed the stop bar while still yellow (at least the front wheel of your vehicle), you didn't run red light. There is a vague language something like "due caution used or not" kind of crap that lets it be officers' call, but it's not necessarily a violation. There are so many seconds (up to 3) before the opposing approach gets green even after it has turned red to you, just to let the vehicles clear who are already at the intersection (ie past the stop bar).