  A detection at the Large Hadron Collider of a light Higgs pseudoscalar would,
if interpreted in a supersymmetric framework, be a smoking gun signature of
non-minimal supersymmetry. In this work in the framework of the Next-to-Minimal
Supersymmetric Standard Model we focus on vector boson fusion and
Higgs-strahlung production of heavier scalars that subsequently decay into
pairs of light pseudoscalars. We demonstrate that although these channels have
in general very limited reach, they are viable for the detection of light
pseudoscalars in some parts of parameter space and can serve as an important
complementary probe to the dominant gluon-fusion production mode. We also
demonstrate that in a Higgsfactory these channels may reach sensitivities
comparable to or even exceeding the gluon fusion channels at the LHC, thus
possibly rendering this our best option to discover a light pseudoscalar. It is
also worth mentioning that for the singlet dominated scalar this may be the
only way to measure its couplings to gauge bosons. Especially promising are
channels where the initial scalar is radiated off a W as these events have
relatively high rates and provide substantial background suppression due to
leptons from the W. We identify three benchmark points that well represent the
above scenarios. Assuming that the masses of the scalars and pseudoscalars are
already measured in the gluon-fusion channel, the event kinematics can be
further constrained, hence significantly improving detection prospects. This is
especially important in the Higgs-strahlung channels with rather heavy scalars,
and results in possible detection at 200/fb for the most favoured parts of the
parameter space.
