Unlike the other offroad missions, there is no specific parked car to trigger this mission. Instead, you have to provide one yourself. Park a Stallion at the entrance to the car park, just outside the red and white gate, and get out and back in. This should trigger the mission. You can often find Stallions parked inside.
Each of the five levels of the car park has four checkpoints in it. They are pretty easy to find, just mind the final jump off the top. Each one only grants you 5 seconds so keep moving.