  We study the geometry and holonomy of semi-Riemannian, time-like metric cones
that are indecomposable, i.e., which do not admit a local decomposition into a
semi-Riemannian product. This includes irreducible cones, for which the
holonomy can be classified, as well as non irreducible cones. The latter admit
a parallel distribution of null $k$-planes, and we study the cases $k=1$ and
$k=2$ in detail. In these cases, i.e., when the cone admits a distribution of
parallel null tangent lines or planes, we give structure theorems about the
base manifold. Moreover, in the case $k=1$ and when the base manifold is
Lorentzian, we derive a description of the cone holonomy. This result is
obtained by a computation of certain cocycles of indecomposable subalgebras in
$\mathfrak{so}(1,n-1)$.
