I assume you don't want to hire an attorney to plea-bargain with the prosecutor to get the ticket reduced or dismissed. So, if you really want to fight it, your best bet is to hire a traffic law attorney who practices in the city or county where you received the ticket.
In the end, there is no guarantee you will win and it will be much more expensive than paying an attorney to get the ticket dismissed or reduced. Remember, at trial, it will be your word against the police officer as to whether you crossed into the intersection when the light was red, and that fact doesn't seem to be in question.
Your defense could be that the car behind you was tailing you and the yellow light was too short, so you were forced to run the light to avoid being rear-ended but, I would imagine the opposing argument would be that you could have stopped in time if you had been driving slower. Just because someone is tailing you is no excuse to speed or run a red light and possibly put others in danger. And trying to argue that the length of the yellow light is too short seems like an uphill battle to me.
A good local traffic law attorney can give you an idea of whether or not you have a case.
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