General aviation turboprop pilot reported a loss off control when taxiing off the runway after landing; resulting in a runway excursion; with the nose gear off the surface and in the grass. The brakes were pumped with braking restored and the aircraft taxied off the grass to parking with no damage.

Narrative

On landing at ZZZ on Runway XX; we experienced a runway excursion. I was right seat; acting as instructor; while the left seat pilot was pilot flying. It was a visual approach backed up by an ILS. The approach and touchdown were textbook: stabilized; soft touchdown on the mains; on centerline and in the touchdown zone. Upon landing we had determined that we would have been able to make an earlier Taxiway (1); but to avoid additional wear on the airplane's brakes; elected to take a further down Taxiway (2). After decelerating to a speed between 5-10 kts.; the pilot flying began to turn off the runway on to Taxiway 1. We had begun the 90 degree turn off the runway with the power levers in beta and after roughly 50-60 degrees of turn; the pilot flying stated that the airplane was not turning. I applied right rudder and brake; and the airplane's trajectory did not change. To avoid striking a taxiway light; I then applied left rudder and left brake to stop the aircraft. The nosewheel of the aircraft responded appropriately and stopped with the nosewheel on the grass. We paused and the pilot flying elected to move the aircraft under its own power out of the grass using left hand turns. Normal braking was restored after pumping the brake pedals several times and we taxied the aircraft to parking. Upon post flight inspection no visible leaks or brake anomalies were observed. No damage was observed on the aircraft or to airport property. After discussion with an A&P familiar with the Conquest II make and model; he suspected low quantity of brake fluid in the master cylinders exacerbated by the fully deflected foot pedal position.Upon inspection of the fluid quantity in the brake master cylinders; it was determined that there was insufficient fluid quantity in the right brake reservoir. There was sufficient; but low levels of fluid int he left brake reservoir.