  Noncentrosymmetric Ce$_{3}$Bi$_{4}$Pd$_{3}$ has attracted a lot of attention
as a candidate for strongly correlated topological material, yet its
experimental ground state remains a matter of contention. Two conflicting
scenarios have emerged from a comparison to prototypical Kondo insulator
Ce$_{3}$Bi$_{4}$Pt$_{3}$: either Ce$_{3}$Bi$_{4}$Pd$_{3}$ is a
spin-orbit-driven topological semimetal or a Kondo insulator with smaller Kondo
coupling than its Pt counterpart. Here we determine the ground state of
Ce$_{3}$Bi$_{4}$Pd$_{3}$ via electrical resistivity measurements under
hydrostatic pressure, which is a clean symmetry-preserving tuning parameter
that increases hybridization but virtually preserves spin-orbit coupling.
Ce$_{3}$Bi$_{4}$Pd$_{3}$ becomes more insulating under pressure, which is a
signature of Ce-based Kondo insulating materials. Its small zero-pressure gap
increases quadratically with pressure, similar to the behavior observed in the
series Ce$_{3}$Bi$_{4}$(Pt$_{1-x}$Pd$_{x}$)$_{3}$, which indicates that Pt
substitution and applied pressure have a similar effect. Our result not only
demonstrates that Kondo coupling, rather than spin-orbit coupling, is the main
tuning parameter in this class of materials, but it also establishes that
Ce$_{3}$Bi$_{4}$Pd$_{3}$ has a narrow-gap Kondo insulating ground state.
