My question involves a traffic ticket from the state of: California

A little while ago I received a ticket for failure to stop at a stop sign, (CA VC 22450(a)), while making a left turn in Los Angeles and my courthouse is the Metropolitan one on South Hill Street. This is what happened.

I was about to make a left turn to look for parking, in what I suppose would be considered a residential area, and I stopped at the stop sign. I looked left first then I looked right and saw a police car stopped in the adjacent street about to enter the intersection. It’s just that the police car was not completely stopped and was rolling into the intersection as I was looking at it. So I assumed that it was waiting for me to hurry up and make my left turn because drivers tend to do that, they start slowly veering into the intersection as they wait for you to make your move, it happens all the time. And in hindsight, perhaps this made me stop at the stop sign for an amount of time that was maybe somewhat relatively brief but that doesn’t mean that I didn’t stop. I’m not stupid enough to just run through a stop sign right in front of police.

So anyways, I make my left turn and next thing I know the police car is pulling me over. FYI, I’ve never been pulled over for a traffic violation, (although I did once receive a camera ticket about 2 years ago), I’ve only ever been pulled over for a fix-it ticket and I don’t even remember when that was because it was so long ago, so I wasn’t totally sure about what the procedures were supposed to be. The police officer takes my license and registration and just leaves to run my records. They didn’t bother to tell me why I was pulled over to begin with and I’m just sitting there wondering what I did wrong. Finally 12 to 15 minutes later the officer comes back to me and says “Sorry, I was supposed to tell you why I pulled you over. You blew through that stop sign. Please sign here.” I was caught off-guard. All I said was “Oh. Really?” I assumed that arguing with the officer right then and there wouldn’t do any good and I didn’t really know what to do. So I just signed and assumed that the only way I could possibly fight this is by going through the city’s set procedures.

So do I have a case and what are my chances for winning if I fight this?

I suppose the officer’s defense would be that the police car was slowly veering into the intersection only because they were concerned about my “reckless” driving. But how would I even relay that whole narrative to the judge anyways, to suggest that the police car slowly rolling into the intersection induced me into maybe not stopping for a sufficient amount of time at the stop sign before making my left turn? Would the judge even care?
And what about the officer not telling me why I was pulled over until the very end? Isn’t this a mistake in official procedure? Does this have any bearing on my case? Would the judge care, especially considering that I can’t really prove this because I have no witnesses?

Advice would be appreciated. Thank you.