Ramp Agent reported a tug brake failure during pushback allowing the aircraft to roll backwards uncontrolled.

Narrative

It was a rainy day we had been waiting for a while for the plane to come in. The plane was parked by the driver and I was crew chief and chocked the plane. The driver brought over the towbar to connect it. He inserted the bypass pin and I lined up the towbar so he can connect it. I moved on to the pushback. I turned it on everything seemed to work fine as I approached the towbar. I was seated and driving the pushback on first gear. As I came closer I came to stop so that the driver could remove the pin in front of the pushback. All of a sudden I felt the pushback start rolling. Everything happened so fast and I could not stop the tractor. I try pressing on the brake but it was too late. Everything happened so fast. I realized the event occurred because of the pushback rolling and my not being unable to stop it. From my perspective; it was an equipment failure. I wholeheartedly believe that my foot was on the brakes while trying to remove the pin. I even remember trying to press down on the brake to stop it but it just kept rolling. I also believe giving the I was position seated I would've felt my leg move because it was bent while pressing the brakes. Additionally; if it had so happened to press the accelerator instead of the brake the pushback would have kicked up in speed; which it did not; and caused a bigger impact. Immediately after the incident; I called the manager on duty to report it. I stayed in position with my foot on the brake because I did not want to move in case it could cause more damage.I believe that we should be more trained in the inspection of all equipment. That it should be something that is done on regular basis. We can prevent these incidents by getting ahead of them. I also think the brake and gas pedal could benefit from having a safety grip or material in order to make equipment safer. In my history of working at the airport; we've seen many belt loaders take off under the plane; and employees have to jump off to prevent impact. I think an extra line of defense would help in cases such as these where our equipment fails to work the way it should.