I live in NY state and my auto insurance lapsed: I've fixed it and my license is still in good standing, should I be proactive about paying the fine? (Crosspost from /r/legaladvice)

My insurance lapsed for a few weeks because I'm a dumbass. I'm now covered again but I never received any mail from the DMV about this and according to the DMV's website my license is still in good standing.

I know there's a chance the lapse will turn up in the DMV's records and I might need to deal with it eventually, but at the same time I don't want to pay ~$400 if I might not need to. Is there any penalty for not paying the fine immediately, given that I now have coverage again and my license still has full driving privileges?