Flight Instructor on training flight with student reported a runway excursion during landing rollout.

Narrative

I was conducting a pre-solo flight lesson by performing takeoffs and landings with my student at ZZZ. On the second touch and go; the student applied too much right rudder immediately following touchdown. At which time; the student abruptly applied left brake causing the aircraft to veer off to the left of the runway and head toward the grass. I immediately took the flight controls from the student and prepared to depart the runway surface due to the forward speed of the aircraft. As the aircraft headed off the runway; the left main landing gear contacted a taxiway light. The left main landing gear fairing was slightly damaged.As a flight instructor; I need to be aware of the student's positioning of their feet on the rudder pedals; as well as applying smooth application of rudder and brake pressure while rolling out during the landing phase in order to stay on the runway centerline. I need to beware of brake usage while landing. I need to make sure the student doesn't shift his/her feet from the bottom of the pedals to the top causing a loss of directional control.