I am in a similar situation. I have a conviction of running a stop sign which resulted in an accident (car crash with another vehicle). I paid the fine for it. No drugs or alcohol were involved. Where in EE application should I declare this?
I also think that this will not be a problem for your PR application. By the way, were there any problems? I also recently had a situation after which I needed a car accident attorney los Angeles. I came there for 2 weeks to chill with friends, and instead my car was damaged. I drove to a green traffic light, and on the right, one very smart driver decided to go faster, and he hit the hood of my car. I was very scared for my friends, but they were safe. Also, I didn't have to mess around with insurance companies for a long time, because they helped me a lot.
You don't need to fight the ticket, but you can go to court and see a judge in an office and ask to have the fine reduced. It's not the same as fighting it and everyone wins.