Gamma-ray bursts (GRBs) are promising as sources of neutrinos and cosmic rays. In the internal shock scenario, blobs of plasma emitted from a central engine collide within a relativistic jet and form shocks, leading to particle acceleration and emission. Motivated by present experimental constraints and sensitivities, we improve the predictions of particle emission by investigating time-dependent effects from multiple shocks. We produce synthetic light curves with different variability timescales that stem from properties of the central engine. For individual GRBs, qualitative conclusions about model parameters, neutrino production efficiency, and delays in high-energy gamma rays can be deduced from inspection of the gamma-ray light curves. GRBs with fast time variability without additional prominent pulse structure tend to be efficient neutrino emitters, whereas GRBs with fast variability modulated by a broad pulse structure can be inefficient neutrino emitters and produce delayed high-energy gamma-ray signals. Our results can be applied to quantitative tests of the GRB origin of ultra-high-energy cosmic rays, and have the potential to impact current and future multi-messenger searches.
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