The law in MI is move over " if you can" or slow down and get over as far as possible. There's been times I couldn't get over but the brakes are alway applied, especially when passing the officer. Not sure if yours were. Can the officer prove your brake lights weren't on ( camera) ? But .... I had issues with state troopers here ( MI ) that were they were far less than honest.
I'm not getting into the details of my run in with them, but it's your word against them. Your probably going to lose the argument ( lawyer will tell you this). Your going to pay the ticket if you try to fight it, maybe get off if you have a good driving record of taking it under advisement and a warning ( no points) but you'll still pay the ticket and court fees.
I just payed $500 to clear a ticket ( points) that I should not have recieved using a lawyer. If I paid the ticket and insurance increases it would have been much more not getting a lawyer involved.
You can go in the web site stated on your ticket and plead with explanation to the court to reduce to no points. I'll still cost you. A lawyer is your best bet to keep the points off your license.
Where did you get it at - what's the court to contact? Finding a lawyer in that jurisdictions would be advised.