  The indirect nuclear spin-spin coupling tensor, $\mathbf J$, between mercury
nuclei in Hg-containing systems can be of the order of few kHz and one of the
largest measured. We conduct an analysis of the physics behind the electronic
mechanisms that contribute to the one- and two-bond couplings $^n {\mathbf
J}_{\mathrm{Hg}-\mathrm{Hg}}$ ($n=1, 2$). We performed calculations for
$J$-couplings in X$_2^{2+}$ and $X_3^{2+}$ ions ($X$ = Zn, Cd, Hg), within
polarization propagator theory, using the random phase approximation (RPA) and
the pure zeroth order approximation (PZOA), with Dirac-Hartree-Fock (DHF) and
Dirac-Kohn-Sham (DKS) orbitals, both at four-component and ZORA levels. We show
that the "paramagnetic-like" mechanism contribute with more than 99.98\% to the
total isotropic component of the coupling tensor. By means of an analysis of
the molecular and atomic orbitals involved in the total value of the response
function, we find that the $s$-type valence atomic orbitals have a predominant
role in the description of the coupling. This fact allows us to develop an
effective model from which quantum electrodynamics (QED) effects on
$J$-coupling in the aforementioned ions can be estimated. The estimated QED
corrections were found in the interval $(0.7; ~ 1.7)$\% of the total
relativistic effect on isotropic one-bond $^1 {\mathbf J}$ coupling and from
the interval $(-0.2; ~ -0.4)$\%, in Zn-containing ions, to $(-0.8; ~ -1.2)$\%,
in Hg-containing ions, of the total isotropic coupling constant in the studied
systems. We also show that estimated QED corrections cast a visible dependence
on the nuclear charge $Z$ of each atom $X$ in the form of a power-law $\propto
Z^5$.
