It also needs to get as close as possible to the top of the hill without going over. L2 is not a stable point: you’re either falling back to Earth or drifting a

It also needs to get as close as possible to the top of the hill without going over. L2 is not a stable point: you’re either falling back to Earth or drifting away. If it goes over it can never get back as it can only fire in one direction - away from Earth (to protect the instruments from the Sun). So it’s a continuous balancing act where it falls downhill towards Earth a bit, then jumps up without going over the edge, rinse and repeat.