  The two classes of 3D, time-reversal-invariant insulators are known to
subdivide into four classes in the presence of glide symmetry. Here, we extend
this classification of insulators to include glide-symmetric Weyl metals, and
find a finer $Z_4\oplus Z$ classification. We further elucidate the smoking-gun
experimental signature of each class in the photoemission spectroscopy of
surface states. Measuring the $Z_4$ topological invariant by photoemission
relies on identifying the glide representation of the initial Bloch state
before photo-excitation - we show how this is accomplished with relativistic
selection rules, combined with standard spectroscopic techniques to resolve
both momentum and spin. Our method relies on a novel spin-momentum locking that
is characteristic of all glide-symmetric solids (inclusive of insulators and
metals in trivial and topological categories). As an orthogonal application,
given a glide-symmetric solid with an ideally symmetric surface, we may utilize
this spin-momentum locking to generate a source of FULLY spin-polarized
photoelectrons, which have diverse applications in solid-state spectroscopy.
Our ab-initio calculations predict Ba$_2$Pb, stressed Na$_3$Bi, and KHgSb to
realize all three, nontrivial insulating phases in the $Z_4$ classification.
