Because they can drive without turning on the headlights to avoid being seen, but they can't control the tail lights. Every time they brake, they'll light up and give their location away.

What the others said. It was a smart tactic to not be seen while following the car. The lights would have clearly given them away.

Because it's pitch black and bright brake lights would easily be seen by the driver of the other car.

Exactly what Rose said, You can turn your head lights out, you can't turn your tail lights out.

At the end of season 2, daryl and carol see a car speeding away, presumably with beth inside, so Daryl smashes the tail lights of the car they found and convinces carol to chase them.

WHY DOES HE SMASH THE LIGHTS? I can't think of any logical explanation, since if they are following the kidnappers, they should bust their front lights, not the tail lights. pls, i need closure