  The puzzle of finding consistent nuclear configurations for explaining both
the decay probabilities and moments of the ${9/2}^-$, ${8}^+$ and ${21/2}^-$
isomers in and around $N=126$ closed shell has been approached in the
generalized seniority scheme. Though $h_{9/2}$ is the dominant orbital near
Fermi energy, the role of configuration mixing from the surrounding $f_{7/2}$
and $i_{13/2}$ orbitals is found to be very important for the consistent
explanation of all the isomeric properties such as the $B(E2)$ rates,
$Q-$moments and $g-$factors. The structural behavior of the closed shell
$N=126$ isotonic isomers turns out to be very similar to the $N=124$ and
$N=128$ isotonic isomers which have two neutron-holes and two
neutron-particles, respectively. This is due to the pairing symmetries of
nuclear many-body Hamiltonian. As a confirmation, the microscopic shell model
occupancies are also calculated for these isomers in $N=126$ chain which
support the generalized seniority results. Additional arguments using the
systematics of odd-proton ${9/2}^-$ states in Tl ($Z=81$), Bi ($Z=83$), At
($Z=85$) and Fr ($Z=87$) isotopes are also presented.
