Air carrier Captain reported a conflict with a GA aircraft after landing at ECP airport requiring immediate brake action by the Captain to avoid a collision. The Tower was closed at the time of the event.

Narrative

We landed Runway 16 at ECP. The Tower was closed. On final; JAX Center turned us over to CTAF. We made normal radio calls. On final I heard a GA aircraft saying they were taxing out of an FBO for Runway 16. We exited 16 at Taxiway P. I remember the First Officer announced on CTAF we were clearing Runway 16 at P. I decided to stop the aircraft once clear of the runway on P short of Taxiway D. The reason I did this was JAX Center asked us to call and cancel our IFR flight plan ASAP as they had another aircraft behind us.Luckily; I decided to stop the aircraft and set the parking brake while we tried to call Center to cancel; this turned out is what saved an accident from occurring. We were unable to contact JAX Center or FSS from the radio on the ground. The First Officer and I decided we would taxi to the gate and call Dispatch or ATC from our phones once parked to cancel. I released the parking brake and began to taxi. Luckily with the distraction of cancelling IFR I forgot to turn my landing lights off after landing. Out of the corner of my eye I saw something moving on Taxiway D to our left lit up with the landing light. It was a single engine GA aircraft taxiing on D to 16. He had no position lights; beacon; or strobe light on. It was night. I hit the brakes and stopped short of Taxiway D and let him pass. I never heard another radio call from him besides the one I heard on final. We then taxied to the gate with no other problems.I'm firmly convinced if I didn't have the landing lights still on; I would have never seen him coming from the left. I 100% believe we would have had a collision on the taxiway if I didn't quickly stop my aircraft.