  Employing the Bogoliubov coefficient summation method and introducing the
gyromagnetic ratio $g\neq 2$ we derive an explicit functional form of
$\mathfrak{Im}V^\mathrm{EHS}_g$, the imaginary part of
Euler-Heisenberg-Schwinger (EHS) type effective action. We show that
$\mathfrak{Im}V^\mathrm{EHS}_g$ is periodic in $g$ for any (quasi-)constant
electromagnetic field configuration, and equal to the imaginary part obtained
using a periodic in $g$ Ramanujan integrand in the proper time representation
of $V^\mathrm{EHS}_g$. This validates the Ramanujan representation of
$V^\mathrm{EHS}_g$ for both real and imaginary parts and allows writing the
effective action in a suitably modified Schwinger proper time format. As a
function of the ratio $b/a$ between ${\mathcal{B}} \to b$ and ${\mathcal{E}}\to
a$ covariant generalizations of EM fields, we explore the singular properties
of $\mathfrak{Im}V^\mathrm{EHS}_g$ at $g=2\pm 4k, k=0,\pm1,\pm2\ldots$
involving the pseudoscalar $ab\equiv \vec{\mathcal{E}}\cdot\vec{\mathcal{B}}$
in perturbative and nonperturbative behavior. We study the $e^-e^+$-decay
vacuum instability, incorporating the physical value of $g-2$ vertex diagrams
when summing infinite irreducible loops. We obtain an effective expansion
parameter $\chi_b=\alpha b/2a$ ($\alpha=e^2/4\pi$), characterizing the onset of
nonperturbative in $g-2$ suppression of vacuum instability. We demonstrate the
$\chi_b$ domains for which perturbative expansion in $\alpha$ breaks down: The
EM vacuum subject to critical electric field strength is stabilized in
magnetic-dominated \lq magnetar\rq\ environments. Considering separately the
case of ${\mathcal{E}}$ and ${\mathcal{B}}$ fields, we generalize to all $g$
the temperature representation of the $V^\mathrm{EHS}_g$ effective action.
