  We present comprehensive multiwavelength radio to X-ray observations of GRB
181201A spanning from $\approx150$ s to $\approx163$ days after the burst,
comprising the first joint ALMA-VLA-GMRT observations of a gamma-ray burst
(GRB) afterglow. The radio and mm-band data reveal a distinct signature at
$\approx3.9$ days, which we interpret as reverse shock (RS) emission. Our
observations present the first time that a single radio-frequency spectral
energy distribution can be decomposed directly into RS and forward shock (FS)
components. We perform detailed modeling of the full multiwavelength data set,
using Markov Chain Monte Carlo sampling to construct the joint posterior
density function of the underlying physical parameters describing the RS and FS
synchrotron emission. We uncover and account for all degeneracies in the model
parameters. The joint RS-FS modeling reveals a weakly magnetized
($\sigma\approx3\times10^{-3}$), mildly relativistic RS, from which we derive
an initial bulk Lorentz factor of $\Gamma_0\approx103$ for the GRB jet. Our
results support the hypothesis that low-density environments are conducive to
the observability of RS emission. We compare our observations to other events
with strong RS detections, and find a likely observational bias selecting for
longer lasting, non-relativistic reverse shocks. We present and begin to
address new challenges in modeling posed by the present generation of
comprehensive, multi-frequency data sets.
