  It was shown recently that, in two Higgs doublet models without $Z_2$
symmetry, extra Yukawa couplings such as $\rho_{tc}$, $\rho_{tt}$ can fuel
enough $CP$ violation for electroweak baryogenesis (EWBG). We revisit an old
proposal where a pseudoscalar $A^0$ has mass between $t\bar c$ and $t\bar t$
thresholds. With $\rho_{tt}$ small, it evades $gg \to A^0 \to h^0(125)Z$
constraints, where approximate alignment also helps. We find this scenario with
relatively light $A^0$ is not yet ruled out, and $cg \to tA^0 \to tt\bar c$ can
probe sizable $\rho_{tc}$ at the LHC, giving access to the second mechanism of
EWBG provided by such models.
