I'm no expert on US law, but it would seem to me that you have two choices. One is to plead guilty by mailing the requested fine amount. The second is to send a letter to the court clerk saying that you are disputing the ticket and would like to have a court date assigned in order to plead your case. You should make a copy of that letter for your records. You then address the letter to the court clerk whose address should be on the ticket. Take that letter to your local post office and ask to have it sent be certified or register mail. That's all you need to do as far as I know.
Once the clerk gets the letter a date should be assigned and you then attend court on that date. That will be your chance to say, gee judge, it wasn't me who ran the light, it was someone else. After that, you're at the mercy of the judge.
I wish you luck.