Don't just pay it if you don't have too and you feel are not guilty. I try to plead down every (5 times now) ticket I have ever gotten in NJ and it works every time and I never used a traffic lawyer.
You likely got a "39:4-81 Failure to observe traffic signal $81 2 points"
My favorite plead down is "39:4-138(l) Improper parking alongside or opposite street excavation or $47 obstruction, causing traffic obstruction (when properly signposted)" + 33 dollar court fee. This carries no points, the state makes the same amount of money and insurance doesn't care at all about them.
NJ just wants your money but doesn't want to work for it. If you give them a even a little speed bump you can win. Call and setup a court date, get prepare to present your case (you have a good driving record you saw the light it was yellow, were not speeding, couldn't stop in time, yellow light is too short for the posted speed limit, etc). On the court date be sure to speak to the prosecutor before the case, you will be provided the chance that day. Present your case the him/her. If offered don't accept a plea to unsafe driving it comes with too many other fines and fees, unsafe driving is only worth it for major fines. 39:4-138 makes them the same money if you just paid the ticket. If they don't let you plea to that or something with the same fine with no points only then just pay the ticket right then and there. Or fight it if you want. Yellow lights should be 1 second for ever 10 mph posted speed limit, you can time the light and fight with clear facts it if the light is not calibrated correctly.
The reason why you should always fight point tickets?
The NJ DM Point system isn't that bad but NJ also have another point system you probably do know about.
Car Insurance Points. CIP
With 12 DMV points you lose your license but with just 7 CIP in 3 years a NJ insurance can drop you because you are considered an at risk driver. And if you can't get a new insurance policy through the preferred market you will have to get one from the high risk market. And unlike DMV points which go down every year, CIP points do not get removed for 3 years from the date of the ticket.
I'm no expert on this point system but it seems bad enough I will go out of my way a little to avoid it.
Link with CIP point schedule because it doesn't exactly follow the DMV point schedule.
http://njpaip.com/nj-mvc-dmv-insurancepoints.html