  In a pseudo-Euclidean space with scalar product $S(\cdot, \cdot)$, we show
that the singularities of projections on $S$-monotone sets and of the
associated Fitzpatrick functions are covered by countable $c-c$ surfaces having
positive normal vectors with respect to the $S$-product. By Zaj\'{\i}\v{c}ek
[24], the singularities of a convex function $f$ can be covered by a countable
collection of $c-c$ surfaces. We show that the normal vectors to these surfaces
are restricted to the cone generated by $F-F$, where $F:=\text{cl range }
\nabla f$, the closure of the range of the gradient of $f$.
