  We study the localization properties of the eigenmodes of the staggered Dirac
operator across the deconfinement transition in finite-temperature
$\mathbb{Z}_3$ pure gauge theory on the lattice in 2+1 dimensions. This allows
for nontrivial tests of the sea-islands picture of localization, according to
which low modes should localize on favorable Polyakov-loop fluctuations in the
deconfined phase of a gauge theory. We observe localized low modes in the
deconfined phase of the theory, both in the real Polyakov-loop sector, where
they are expected, and in the complex Polyakov-loop sectors, where they are
not. Our findings expose the limitations of the standard sea-islands picture,
and call for its refinement. An improved picture, where spatial hopping terms
play a more prominent role, is proposed and found to be in excellent agreement
with numerical results.
