Fortunately I have no experience with the Calif. traffic courts since moving here 15 years ago.

But in NJ there was an option to plead 'guilty but with an explanation' and there may be something similar here. In your case I'd think the explanation would be to emphasize that you were on a bicycle and therefore mainly endangering yourself and that since it is a 'T' intersection your path was not directly conflicting with any other traffic entering the intersection on the green (I'd have a map of the street available in case the judge asks for one). Based on those mitigating factors you hope the size of the fine might be reduced.

Appearing in court instead of just mailing in a payment also has the advantage that you can verify that this is being recorded as a cycling offense and should therefore not impact insurance rates.