If physics beyond the Standard Model (BSM) explains the 4.2σ difference between the Standard Model and measured muon anomalous magnetic moment a_μ, minimal flavor violation predicts a shift in the analog quantity for the τ lepton aτ 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 F₂(s) at s = (10  GeV)² and report the first complete two-loop prediction of Re F^eff₂ (100  GeV²) = -268.77(50) × 10^-6 for resonant τ-pair production in e⁺e^- → Υ(nS) → τ⁺τ^-, n = 1, 2, 3. Re F^eff₂ can be measured from e^--helicity-dependent transverse and longitudinal asymmetries in τ-pair events, which requires a longitudinally polarized e^- beam. We discuss how Belle II asymmetry measurements could probe a^BSM_τ 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_τ.