  Quantum electrodynamics in $1 + 1$ space-time dimensions is analytically
solvable for massless fermions, while no solution is known for massive
fermions. Employing the classical-statistical approach, we simulate the
real-time dynamics on a lattice using Wilson fermions with mass $m$ at gauge
coupling $g$. It is shown that quantitative properties of the massless
Schwinger model are emerging in the limit of large $g/m$. We investigate two
scenarios corresponding to opposite charges which are either held fixed or
moving back-to-back along the light cone, as employed in effective descriptions
for jet energy loss and photon production in the context of heavy-ion
collisions. Remarkably, we find that the dynamics is rather well described by
the massless limit for a wide range of mass values at fixed coupling. Moreover,
our study shows that previous approximate scenarios with external charges on
the light cone rather accurately capture the self-consistent dynamics of the
energy conserving simulation.
