Eclipse EA 500 First Officer reported a taxiway excursion as a result of a loss of brake pedal authority on the right brake during taxi at a non-towered airport. The Captain took over control and aggressively stopped the aircraft after swerving off the taxiway surface. The crew evacuated from the aircraft and there was no damage to taxiway lights.

Narrative

At XA:10 on Day 0; Pilot In Command and I (Second In Command) departed ZZZ to return back to ZZZ1 after dropping off passengers. After we finished the Before-Taxi Checklist; I took control of the aircraft as I was the Pilot Flying. I began taxiing on the ramp at around three kts ground speed to the right; using right differential braking to maneuver around a Gulfstream that had recently deplaned. Upon reaching Taxiway 1; I turned left and entered Taxiway 1 to Runway X. While on the taxiway; I completed the taxi checks; including a brake test. Both brakes were operative.I continued taxiing on [Taxiway] 1 with the throttles at idle; since a downhill gradient existed and extra power was unnecessary. As I continued taxiing past the last turnoff; I noticed that I was gaining more momentum than I preferred; and gently applied brakes. The left brake had authority; but the right brake pedal sank to the floor. I immediately began pumping the brake to induce more hydraulic pressure. At this point; I applied full right rudder. As I was applying right rudder and pumping the right brake; Pilot In Command noticed that I was departing centerline to the left. He asked what I was doing; and immediately applied full brakes on his side. The plane swerved sharply to the left; and departed the taxiway into the gravel; and came to a stop. Neither pilots nor the plane was damaged. It should be noted that the castoring nosewheel had snapped free and was at an approximate 70 to 90 degree angle to the left as the plane came to a rest.This issue had been squawked by another pilot earlier in the week; and we briefed the item prior to our departure from ZZZ1 during preflight. The squawk had been signed off by the contract mechanic and Pilot In Command showed me a letter of permission from our Director of Operations who possessed operational control at the time; releasing us to fly. We needed this because we do not have a Director of Maintenance. The brake test in ZZZ1 prior to our outbound leg was successful and normal.I believe that if I had spoken up immediately; I could have verbally alerted Pilot In Command to the condition a few seconds sooner; and it would have avoided the startle effect that he experienced as he looked up and saw us departing centerline. I could have immediately surrendered controls; instead of instinctively trying to solve the situation myself. Though these are points of experience gained; I know there was absolutely nothing that would have prevented us from leaving the paved taxi surface with the brakes in the condition that they were in. It was either straight ahead to mow over a sign; or to the left; evenly-spaced in between two taxi lights that remained untouched.