ABSTRACT Gamma-ray observations have revealed strong variability in blazar luminosities in the gamma-ray band over time-scales as short as minutes. We show, for the first time, that the correlation of the spectrum with intensity is consistent with the behaviour of the luminosity variation of blazar spectral energy distributions (SEDs) along a blazar sequence for low synchrotron peak blazars. We show that the observational signatures of variability with flux are consistent with wakefield acceleration of electrons initiated by instabilities in the blazar accretion disc. This mechanism reproduces the observed time variations as short as 100 s. The wakefield mechanism also predicts a reduction of the electron spectral index with increased gamma-ray luminosity, which could be detected in higher energy observations well above the inverse Compton peak.