The light curves of the prompt phase of gamma-ray bursts (GRBs) exhibit erratic and diverse behaviour, often with multiple pulses. The temporal shape of individual pulses is often modelled as ‘fast rise exponential decay’ (FRED). Here, we propose a novel fitting function to measure pulse asymmetry. We perform a time-resolved spectrum analysis on a sample of 75 pulses from twenty-seven GRBs that the Fermi Gamma-ray Burst Monitor has identified. When multi-pulse bursts are taken into account, a distinct behaviour becomes evident: the first pulses have the most symmetric-like lightcurve, while subsequent pulses show an increase in the asymmetry parameter, leading to a more FRED-like form. Furthermore, we correlate pulse temporal and spectral shapes after fitting the spectra with the classical “Band" function. A moderate positive Spearman correlation between pulse asymmetry and the low-energy spectral index αmax (where the maximum is taken over all time bins that cover the pulse shape) is identified. An overlapping emission mechanism is indicated by the fact that ∼ 64% of the GRB pulses fall within the limits of the slow-cooling synchrotron and non-dissipative photospheric emission models. Thus, our findings offer a compelling hint towards understanding the origin of GRB pulses.