Sub‐daily rainfall intermittency is virtually ubiquitous, with multiple periods of rain in a day being separated by temporary cessations. This phenomenon remains only partly explored. A significant question is whether the on–off sequence of rainfalls can be regarded as stochastic, as presumed in some common approaches to rainfall disaggregation, such as daily to hourly or hourly to sub‐hourly disaggregation, or whether there is an underlying sequence of rainfalls and cessations, related perhaps to other diurnal changes in rainfall. At two Australian locations, the timing of the longest cessation—whether it was the first, second, or a subsequent cessation on any day—was used to test this. Pluviograph data revealed up to 24 rainfall cessations per day. Analysis showed that the first cessation was in most cases the longest on a rainy day, and less often, this was the second, third, or subsequent cessation. Moreover, the decline in the mean duration of cessations was well‐fitted by a logarithmic function of their position in the daily series of cessations. In addition, both field sites exhibited evidence of diurnal cycles in amount, intensity, and frequency of rainfall, and also in the extent of intermittency in the form of intra‐day rainfall cessations. Whilst additional evidence is needed, it is hypothesised that these findings with respect to rainfall arrival may reflect a progressive and intermittent onset and decay of convection and moisture convergence, together with progressive changes in the scale of eddy turbulence, linked to the daily transitions in net radiation and local air buoyancy and uplift. The results suggest that wholly stochastic rainfall disaggregation procedures may be missing key aspects of diurnal rainfall behaviour. Exploration of these phenomena at additional locations seems warranted.