New Mexico absolutely does not have a pay at the roadside option. That’s regular Mexico.
You have two options statewide. Sign a penalty assessment admitting guilt. You may then mail in the fine, pay on the courts website, etc. You risk getting an arrest warrant issued if you do not send it in within 30 days.
Option 2, see a judge. If you are from New Mexico, you get a court date. Otherwise, you must go meet a judge right then. You will probably be asked to post bond equal to the fine if you wish to set up a different court date.
But there is simply not an option to pay at roadside. The woman was an ass looking for a cause who lead a speeding chase through an area where she could have killed tourists, motorcyclists, bike riders, etc. Her kids are no more valuable than mine.
She could have signed the ticket with no danger. If she fled, she could have driven normally into town. She was the danger here. Not the guy going for her tires. At the 2nd stop, it would have been better to deploy a spikebelt in front of her van though. She had already fled once.