A unique sequence of 120 almost identical plasmas in the Joint European Torus (JET) recently provided two orders of magnitude more statistically equivalent data than ever previously available. The purpose was to study movement of eroded plasma-facing material from JET's new Beryllium wall, but it has allowed the statistical detection of otherwise unobservable phenomenon. This includes a sequence of resonant-like waiting times between edge-localised plasma instabilities (ELMs), instabilities that must be mitigated or avoided in large magnetically confined plasmas such as those planned for ITER. Here, we investigate the cause of this phenomenon, using the unprecedented quantity of data to produce a detailed picture of the plasma's behaviour. After combining the data, oscillations are clearly observable in the plasma's vertical position, in edge losses of ions, and in Beryllium II (527?nm) light emissions. The oscillations are unexpected, are not obvious in data from a single pulse alone, and are all clearly correlated with each other. They are likely to be caused by a small vertical oscillation that the plasma control system is not reacting to prevent, but a more complex explanation is possible. The clearly observable but unexpected link between small changes in the plasma's position and changes to edge-plasma transport and stability suggest that these characteristics cannot always be studied in isolation. It also suggests new opportunities for ELM mitigation and control that may exist.