Ultra-high-energy cosmic rays and high-energy astrophysical neutrinos are
routinely detected, but their sources remain unknown.  Gamma-ray bursts
(GRBs) have long been considered attractive candidate sources.  Recently, the
lack of neutrinos detected in coincidence with known GRBs has motivated
revisions of the multi-messenger emission mechanism --- gamma rays, cosmic rays,
neutrinos --- from within the GRB jet.  By embedding this revised mechanism in a
simulation of multiple emission regions within the jet, we obtain a robust
prediction for the minimal diffuse GRB neutrino flux, likely within the
reach of the planned detector upgrade, IceCube-Gen2.  Further, we show that, by
looking for features in the shape of the GRB gamma-ray light curve, we can
assess whether a particular burst is likely to be an intense neutrino
source.