At Everest’s summit (8,848 m), gravity is about 0.28 % weaker than at sea level, reducing the restoring force and lengthening the period.
Thinner air means less aerodynamic damping, so the pendulum loses energy more slowly, also tending to increase the period.
Extreme cold contracts the pendulum rod, slightly shortening its effective length, which would decrease the period.
The gravity and damping effects dominate; overall, the pendulum’s oscillation period increases when moved from ground level to the summit of Mount Everest.