  If physics beyond the Standard Model (BSM) explains the $4.2\sigma$
difference between the Standard-Model and measured muon anomalous magnetic
moment, $a_{\mu}$, minimal flavor violation predicts a shift in the analog
quantity for the $\tau$ lepton, $a_{\tau}$, at the $10^{-6}$ level, and even
larger effects are possible in generic BSM scenarios such as leptoquarks. We
show that this produces equivalent BSM deviations in the Pauli form factor,
$F_2(s)$, at $s=(10\,\text{GeV})^2$, and report the first complete two-loop
prediction of $\text{Re}\, F_2^\text{eff}(100\,\text{GeV}^2)=-268.77(50)\times
10^{-6}$ for resonant $\tau$-pair production in $e^+e^-\rightarrow \Upsilon(nS)
\rightarrow$ $\tau^+\tau^-$, $n=1,2,3$. $\text{Re}\, F_2^\text{eff}$ can be
measured from $e^-$-helicity-dependent transverse and longitudinal asymmetries
in $\tau$-pair events, which requires a longitudinally polarized $e^-$ beam. We
discuss how Belle II asymmetry measurements could probe $a_{\tau}^\text{BSM}$
at $10^{-6}$, assuming such a polarization upgrade of the SuperKEKB $e^+e^-$
collider, and conclude by outlining the next steps to be taken in theory and
experiment along this new avenue for exploring realistic BSM effects in
$a_\tau$.
