Context. There has been significant technological and scientific progress in our ability to detect, monitor and model the physics of gamma-ray bursts (GRBs) over the 50 years since their first discovery. However, the dissipation process thought to be responsible for their defining prompt emission is still unknown. Recent efforts have focused on investigating how the ultrarelativistic jet of the GRB propagates through the progenitor's stellar envelope, for different initial composition shapes, jet structures, magnetisation, and -consequently -possible energy dissipation processes. Study of the temporal variability -in particular the shortest duration of an independent emission episode within a GRB -may provide a unique way to discriminate the imprint of the inner engine activity from geometry and propagation related effects. The advent of new high-energy detectors with exquisite time resolution now makes this possible. Aims. We aim to characterise the minimum variability timescale (MVT) defined as the shortest duration of individual pulses that shape a light curve for a sample of GRBs in the keV-MeV energy range and test correlations with other key observables, such as the peak luminosity, the Lorentz factor, and the jet opening angle. We compare these correlations with predictions from recent numerical simulations for a relativistic structured -possibly wobbling -jet and assess the value of temporal variability studies as probes of prompt-emission dissipation physics. Methods. We used the peak detection algorithm mepsa to identify the shortest pulse within a GRB time history and preliminarily calibrated mepsa to estimate the full width half maximum (FWHM) duration. We then applied this framework to two sets of GRBs: