Some experiments with a hp 5071A cesium frequency standard (std-perf tube, not high-perf tube).
When a 5071 goes from normal mode to standby mode there is an unexplained frequency jump, there is a significant reduction in short-term noise, and the frequency begins to drift.
Note normal mode (cesium lock) has far more short-term noise but stays at constant average frequency. In standby mode (cesium unlock) the quartz short-term noise is very low but the frequency wanders.