Running a red light...
Based on your story... proceeding through a yellow advance left signal you did not run a red light...
As I understand the definition of the offence, running a red light means your vehicle was entirely behind the white line when the light turned red...
If you are in the intersection and it goes red your okay. If you enter the intersection while the light was yellow you are okay. Also the cop had to witness the offence. So say you run a yellow and get in an accident. The cop can charge you with running a red, but since he didn't witness it, he can't swear information in court. Someone who actually saw you do it.
Get a copy of the statute you are charged with and read it thoroughly. You might be able to get it tossed all together. Speeding can get knocked down to a no points level, but running a red is different. Even if you pay less they still take the three points. So in that case, is it worth even going to court?
That being said, if you were in the left turn lane, and were like the fourth car making that left on a yellow... shame on you and I don't have any sympathy. That's just inconsiderate and shows no appreciation for helping traffic flow...