  Electronic nematicity in correlated metals often occurs alongside another
instability such as magnetism. As a result, the question remains whether
nematicity alone can drive unconventional superconductivity or anomalous
(quantum critical) transport in such systems. In FeSe, nematicity emerges in
isolation, providing a unique opportunity to address this question. Studies to
date, however, have proved inconclusive; while signatures of nematic
criticality are observed upon sulfur substitution, they appear to be quenched
under the application of pressure due to the emergent magnetism. Here, we study
the temperature and pressure dependence of the low-temperature resistivity of
FeSe$_{1-x}$S$_{x}$ crystals at $x$ values just beyond the nematic quantum
critical point. Two distinct components to the resistivity are revealed; one
whose magnitude falls with increasing pressure and one which grows upon
approaching the magnetic state at higher pressures. These findings indicate
that nematic and magnetic critical fluctuations in FeSe$_{1-x}$S$_{x}$ are
completely decoupled, in marked contrast to other Fe-based superconductors, and
that nematic fluctuations alone may be responsible for the transport signatures
of quantum criticality found in FeSe$_{1-x}$S$_{x}$ at ambient pressure.
