An air taxi pilot reported brake failure while taxiing resulted in a temporary loss of control and taxiway excursion.

Narrative

I started Aircraft X at the hangers on the west end of ZZZ. Upon starting both engines; I let Aircraft Y and Aircraft Z taxi ahead of me and performed a brake check before commencing taxi to the hold short line of Taxiway 1. From there; the pilot of Aircraft Y obtained a taxi clearance from ZZZ Ground. Upon reaching the hold short line of Taxiway 1 I used the engines to slow; and then both brakes to slow down further; then primarily right brake and rudder to make the right hand turn onto Taxiway 1 in the direction of Taxiway 2. Both brakes felt slightly soft; but seemed to be operational during both checks. Approaching the intersection of taxiways 1 and 2; I pulled power to roughly 600rpms on both engines to slow; not yet using any brakes. Upon reaching the corner; I applied the left rudder and tried to apply the left brake as well to make the turn. At this point the left brake felt very soft and unresponsive. I continued to apply full left rudder and verified the left engine was at idle; and slightly increased power on my right engine to attempt to turn the airplane using differential thrust. I could not get the airplane to turn sharp enough to stay on Taxiway 2. At this point I tried to apply both brakes and crossed the Taxiway centerline on 2. As running off of the taxiway looked like it was possible at this point I pulled both engines back to idle and pulled both mixtures to cutoff to make every attempt to stop before going off of the taxiway. As the right engine was spinning down to shutdown my prop struck a taxiway light just prior to the aircraft coming to a stop. After reporting to ZZZ Ground about the situation; ZZZ Airport Fire Department arrived; I accessed the airplane and called an FBO to bring a tug. We then towed the aircraft backwards unto taxiway 2; and Taxiway 1 back to the Hangers.