  We investigate the possibility of detectable 2-Higgs Doublet Model (2HDM)
type-II cross-sections at the High-Luminosity phase of the Large Hadron
Collider (HL-LHC) for the production of the Standard Model (SM)-like Higgs
boson ($h$) in association with a single top (anti)quark over the parameter
space region corresponding to the so-called `wrong-sign solution' of the bottom
(anti)quark Yukawa coupling. We isolate the latter by using the toolbox
Magellan, which performs Markov Chain Monte Carlo (MCMC) scans in the presence
of all current theoretical and experimental constraints, which relevance is
accounted for accurately by using built-in Bayesian statistical methods. It is
found that the allowed points in the 2HDM type-II parameter space of the
aforementioned kind would not only provide inclusive rates considerably above
those of the equivalent SM process but also distributions in several
kinematical observables that are very different from the SM, both of which can
help disentangle the SM from the 2HDM hypothesis. This difference is a
consequence of the bottom-gluon fusion sub-process, which in the 2HDM becomes
dominant over all others, with the latter remaining very close to the SM
yields. We prove that this phenomenology would be observable at the HL-LHC for
the illustrative example of $h$ to bottom-antibottom quark decays.
