  We study invariant gauge fields over the 4-dimensional non-reductive
pseudo-Riemannian homogeneous spaces G/K recently classified by Fels & Renner
(2006). Given H compact semi-simple, classification results are obtained for
principal H-bundles over G/K admitting: (1) a G-action (by bundle
automorphisms) projecting to left multiplication on the base, and (2) at least
one G-invariant connection. There are two cases which admit nontrivial examples
of such bundles and all G-invariant connections on these bundles are
Yang-Mills. The validity of the principle of symmetric criticality (PSC) is
investigated in the context of the bundle of connections and is shown to fail
for all but one of the Fels-Renner cases. This failure arises from degeneracy
of the scalar product on pseudo-tensorial forms restricted to the space of
symmetric variations of an invariant connection. In the exceptional case where
PSC is valid, there is a unique G-invariant connection which is moreover
universal, i.e. it is the solution of the Euler-Lagrange equations associated
to any G-invariant Lagrangian on the bundle of connections. This solution is a
canonical connection associated with a weaker notion of reductivity which we
introduce.
