  We present the results of broadband dielectric spectroscopy of GaMo$_4$S$_8$,
a lacunar spinel system that recently was shown to exhibit non-canonical,
orbitally-driven ferroelectricity. Our study reveals complex relaxation
dynamics of this multiferroic material, both above and below its Jahn-Teller
transition at T$_{\textrm{JT}}=47$ K. Above T$_{\textrm{JT}}$, two types of
coupled dipolar-orbital dynamics seem to compete: relaxations within
cluster-like regions with short-range polar order like in relaxor
ferroelectrics and critical fluctuations of only weakly interacting dipoles,
the latter resembling the typical dynamics of order-disorder type
ferroelectrics. Below the Jahn-Teller transition, the onset of orbital order
drives the system into long-range ferroelectric order and dipolar dynamics
within the ferroelectric domains is observed. The coupled dipolar and orbital
relaxation behavior of GaMo$_4$S$_8$ above the Jahn-Teller transition markedly
differs from that of the skyrmion host GaV$_4$S$_8$, which seems to be linked
to differences in the structural distortions of the two systems on the
unit-cell level.
