  The mean-square charge radii of $^{207,208}$Hg ($Z=80, N=127,128$) have been
studied for the first time and those of $^{202,203,206}$Hg ($N=122,123,126$)
remeasured by the application of in-source resonance-ionization laser
spectroscopy at ISOLDE (CERN). The characteristic \textit{kink} in the charge
radii at the $N=126$ neutron shell closure has been revealed, providing the
first information on its behavior below the $Z=82$ proton shell closure. A
theoretical analysis has been performed within relativistic Hartree-Bogoliubov
and non-relativistic Hartree-Fock-Bogoliubov approaches, considering both the
new mercury results and existing lead data. Contrary to previous
interpretations, it is demonstrated that both the kink at $N=126$ and the
odd-even staggering (OES) in its vicinity can be described predominately at the
mean-field level, and that pairing does not need to play a crucial role in
their origin. A new OES mechanism is suggested, related to the staggering in
the occupation of the different neutron orbitals in odd- and even-$A$ nuclei,
facilitated by particle-vibration coupling for odd-$A$ nuclei.
