Edge localised mode (ELM) measurements from reproducibly similar plasmas in the JET tokamak, which differ only in their gas puffing rate, are analysed in terms of the pattern in the sequence of waiting times between successive ELMs. It is found that the category of ELM defined empirically as Type I - typically more regular, less frequent, and having larger amplitude than other ELM types - embraces substantially different ELMing processes. Delay time embedding reveals a transition between distinct phase space structure, implying a transition between distinct underlying physical processes. By quantifying the structure in the sequence of waiting times of ELMs for the first time, we establish a relationship between a control parameter (gas puffing rate) and impulsive events in these nonlinearly coupled multiscale plasmas.