  Colourings and flows are well-known dual notions in Graph Theory. In turn,
the definition of flows in graphs naturally extends to flows in oriented
matroids. So, the colour-flow duality gives a generalization of Hadwiger's
conjecture about graph colourings, to a conjecture about coflows of oriented
matroids. The first non-trivial case of Hadwiger's conjecture for oriented
matroids reads as follows. If $\mathcal{O}$ is an $M(K_4)$-minor free oriented
matroid, then $\mathcal{O}$ has a now-where $3$-coflow, i.e., it is
$3$-colourable in the sense of Hochst\"attler-Ne\v{s}et\v{r}il. The class of
generalized series parallel ($GSP$) oriented matroids is a class of
$3$-colourable oriented matroids with no $M(K_4)$-minor. So far, the only
technique towards proving that all orientations of a class $\mathcal{C}$ of
$M(K_4)$-minor free matroids are $GSP$ (and thus $3$-colourable), has been to
show that every matroid in $\mathcal{C}$ has a positive coline. Towards proving
Hadwiger's conjecture for the class of gammoids, Goddyn, Hochst\"attler, and
Neudauer conjectured that every gammoid has a positive coline. In this work we
disprove this conjecture by exhibiting an infinite class of strict gammoids
that do not have positive colines. We conclude by proposing a simpler technique
for showing that certain oriented matroids are $GSP$. In particular, we recover
that oriented lattice path matroids are $GSP$, and we show that oriented
cobicircular matroids are $GSP$.
