Corporate flight crew reported confusion finding a taxiway after ATC instructed them to clear the runway for landing traffic.
Synopsis
Corporate flight crew reported confusion finding a taxiway after ATC instructed them to clear the runway for landing traffic.
Narrative
It was a two and half hour ground delay in ZZZ for a departure to San Diego (SAN). It was very busy airspace. My co-captain and I finally landed and boarded our passengers In San Diego. It was now very dark night. Passengers were well briefed. I was the pilot not flying the return trip back to ZZZ. We spent several minutes looking at taxi and navigation charts together and discussing our plan before starting engines. We have not been to San Diego in a couple years. It was still very busy in San Diego. Not much spacing between aircraft exiting the runway and landing or departing aircraft. Air Traffic Control is doing an amazing job.We start the engines and taxi out behind multiple corporate jets waiting for departure on the north side of runway 27; full length from taxiway C1. There were also multiple airlines waiting for departure on the south side of runway 27. Departing aircraft were instructed to line up and wait as soon as the landing aircraft flew past the first perpendicular taxiways. Runway 27 has a 1810' long displaced threshold; so landing aircraft are still high as they begin flying over the displaced threshold perpendicular to taxiway C1.It was our turn to 'line-up and wait' on runway 27 from taxiway C1 as soon as landing traffic passed our position. We were also told to be ready for an immediate departure. I told tower we will be ready to go. We taxied onto the runway and completed our takeoff checklist. We stopped on the runway; were focused and ready to go for takeoff. This is where trouble began. The landing airliner ahead of us missed their taxiway; possibly two opportunities; for an expedited exit off the runway. Landing traffic was getting closer behind us. Tower declared that this was not going to work for us and instructed us to immediately exit the runway via taxiway C2. I read back that we would exit without delay on C2. It felt like we had just seconds to exit. Both the flying pilot and I were having difficulty locating taxiway C2 off our right side. There did not seem to be any lead off lights or anything to assist us. We found ourselves turning too early and taxied into the 'ovals' between C1 and C2. The landing aircraft behind us had to go-around.We were able to maneuver out of the ovals without hitting any obstacles or causing any damage. It took us what seemed to be about a minute to clear the oval and exit off runway 27 onto C1. We were able to depart San Diego about 30 minutes later without any other issues.What was the cause of our issues? Air traffic control was on their game and did an amazing job. The two of us pilots were so focused in the moment for an immediate departure that we did not expect to have to exit the runway via C2. We knew where C2 was; but we did not look for it while stopped relative to our current position on the runway. This situation of possibly having to exit the runway was not discussed in our briefing. Both of us tried looking for lead in lines or lights but for some reason it was simply dark. There was a working taxiway location sign for C2; but we just didn't start our turn off the runway after the taxiway location sign. Trying to get off the runway in a rush from a stopped position did not help the situation either. All this happened so quickly as one would expect in an extremely saturated airport and airspace with one runway. We are both professional corporate pilots and this event was on us and no one else. Similar situations will be briefed in the future.
Second reporter narrative
We were holding short of Runway 27 on taxiway C1 awaiting takeoff clearance.Tower cleared us into position and hold and told us to be ready for an immediate takeoff and said traffic was on a 3 mile final. We quickly taxied into position and prepared for an immediate takeoff.The airplane that had just landed; just ahead of the tower clearing us into position for takeoff missed their assigned turnoff taxiway and had to continue down the runway to another farther down the runway taxiway.The Tower said 'this is not going to work' and told us to immediate get off the runway onto taxiway C2.We taxied a few hundred feet down the runway (rapidly) and turned when we saw the C2 taxiway sign but we turned too soon and ended up being in what the Tower called the 'Oval' area and were not clear of the runway. The Tower told the traffic on final to go around and we had to turn out of the oval area and go another 50 feet to then turn onto taxiway C2 and clear the runway.There appeared to be no yellow lead in stripe from the runway onto taxiway C2 making it hard to locate at night.I suppose there was a blunder on numerous sources:1) The tower was really packing in the arrivals and departures as close as possible.2) The tower told the landing airplane to turnoff on a certain taxiway and they acknowledged to the tower they would do so.3) The landing airplane went past the assigned taxiway and the tower was forced to get us off the runway ASAP for the next landing plane.4) We missed the taxiway we needed to take to get off the runway immediately because we were hurrying too much and and there was no yellow lead stripe onto the taxiway and the tower had to issue a go around to the landing airplane. If it had been daylight we would not have turned off the runway at the wrong location.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.