  We study the localisation properties of the eigenmodes of the staggered Dirac
operator in finite-temperature $\mathbb{Z}_2$ gauge theory on the lattice in
2+1 dimensions. We find that the low modes turn from delocalised to localised
as the system crosses over from the confined to the deconfined phase in the
"physical" sector (positive average Polyakov loop), while they remain
delocalised in the "unphysical" sector (negative average Polyakov loop). This
confirms that the close connection between deconfinement and localisation of
the low Dirac modes in the physical sector, already observed in other models,
holds also in the simplest gauge theory displaying a deconfinement transition.
We also observe a clear correlation of localised modes with fluctuations of the
Polyakov loop away from the ordered value, as expected according to the
"sea/islands" picture of localisation, and with clusters of negative
plaquettes. A novel finding is the presence of localised modes at the high end
of the Dirac spectrum in all phases/sectors of the theory.
