  Recently, extra dimensional SUSY GUT models have been proposed in which
compactification of the extra dimension(s) leads to a breakdown of the gauge
symmetry and/or supersymmetry. We examine a particular class of
higher-dimensional models exhibiting supersymmetry and SU(5) or SO(10) GUT
symmetry. SUSY breaking occurs on a hidden brane, and is communicated to the
visible brane via gaugino mediation. Non-universal gaugino masses are developed
at the compactification scale as a consequence of a restricted gauge symmetry
on the hidden brane. In this case, the compactification scale is at or slightly
below the GUT scale. We examine the parameter space of such models where
gaugino masses are related due to a Pati-Salam symmetry on the hidden brane. We
find limited but significant regions of model parameter space where a viable
spectra of SUSY matter is generated. Our results are extended to the more
general case of three independent gaugino masses; here we find that large
parameter space regions open up for large values of the U(1) gaugino mass M_1.
We also find the relic density of neutralinos for these models to be generally
below expectations from cosmological observations, thus leaving room for hidden
sector states to make up the bulk of cold dark matter. Finally, we evaluate the
branching fraction BF(b -> s gamma) and muon anomalous magnetic moment a_\mu.
