Aims. The aim of this work is to identify the mechanism driving pulsations in hard X-ray (HXR) and microwave emission during solar flares. Using combined HXR and microwave observations from Solar Orbiter/STIX and EOVSA, we investigate an X1.3 GOES class flare, 2022-03-30T17:21:00, which displays pulsations on timescales evolving from ∼7 s in the impulsive phase to ∼35 s later in the flare. Methods. We analysed the temporal, spatial, and spectral evolution of the HXR and microwave pulsations during the impulsive phase of the flare. We reconstructed images for individual peaks in the impulsive phase and performed spectral fitting at high cadence throughout the first phase of pulsations. Results. Our imaging analysis demonstrates that the HXR and microwave emission originates from multiple sites along the flare ribbons. The brightest sources and the location of the emission change in time. Through HXR spectral analysis, the electron spectral index is found to be anti-correlated with the HXR flux, showing a “soft-hard-soft” spectral index evolution for each pulsation. The timing of the associated filament eruption coincides with the early impulsive phase. Conclusions. Our results indicate that periodic acceleration and/or injection of electrons from multiple sites along the flare arcade is responsible for the pulsations observed in HXR and microwave emission. The evolution of pulsation timescales is likely a result of changes in the 3D magnetic field configuration over time related to the associated filament eruption.