Exclusive decays of the Higgs boson to a pseudoscalar quarkonium and a pair of leptons, $h\to \eta_{c,b}\ell^+\ell^-$ are rare and can be substantially enhanced in a scenario which includes a light CP-odd Higgs $A$ ($m_A\lesssim m_h$) which makes them experimentally appealing. We illustrate that feature in two Higgs doublet models (2HDM) and show that $\mathcal{B}(h\to \eta_{c,b}\tau^+\tau^-)$ can be an order of magnitude larger than in the Standard Model, i.e. $\mathcal{O}(10^{-6}\div10^{-5})$.