  We show that \emph{vertical} contributions to (possibly semistable)
Tanaka-Thomas-Vafa-Witten invariants are well defined for surfaces with
$p_g(S)>0$, partially proving conjectures of \cite{TT2} and \cite{T}. Moreover,
we show that such contributions are computed by the same tautological integrals
as in the stable case, which we studied in \cite{L}. Using the work of Kiem and
Li, we show that stability of universal families of vertical Joyce-Song pairs
is controlled by cosections of the obstruction sheaves of such families.
