Volcanic eruption columns typically have unsteady source conditions, where mass and heat fluxes from the vent evolve or fluctuate on time scales from seconds to hours. However, integral plume models routinely assume source conditions that are statistically stationary, and the degree to which source unsteadiness influences the mechanics of column rise and air entrainment has not been established with quantitative predictions. We address this knowledge gap by examining eruptions with varying unsteady character at Sabancaya Volcano, Peru. Using a novel tracking algorithm based on spectral clustering, we track the spatiotemporal evolution of coherent turbulent structures in columns using ground-based, thermal infrared imagery. For turbulent structures tracked in time and space, we calculate the power law decay exponent of excess temperature with height. In general, the starting pulses of transient events are characterized by power law exponents matching theoretical predictions for an instantaneous point release of buoyancy (i.e. a thermal), which evolve with sustained emissions to values consistent with steady plumes. Our results support previous findings from field evidence and laboratory experiments that entrainment and gravitational stability in unsteady volcanic columns are inadequately captured by time-averaging or constant entrainment coefficients. We propose a quantitative definition for column source unsteadiness which captures the timing and magnitude of source fluctuations on time scales that influence entrainment mechanics, and which provisionally predicts our observed differences in power law behavior. We argue for systematic experimental and numerical studies of the relationship between source unsteadiness and entrainment to develop unsteady entrainment parameterizations for integral plume models.