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The β-ray angular distributions from purely spin aligned 12B and 12N nuclei were precisely remeasured to determine a new limit of the G-parity irregular induced tensor form factor in weak nucleon axial vector currents and to study the in-medium mass renormalization of nucleons through the axial charge. A more reliable result on the induced tensor term was obtained as -0.31 ≤2MfT/fA ≤0.02 at a 90% confidence level. This result is consistent with the theoretical prediction in the framework of which the form factor is proportional to the mass difference between the up and down quarks. The axial charge of the axial vector current was determined to be y = 4.9 ±0.10, which may disclose an in-medium mass reduction of the decaying nucleon of (16 ±4)% at a 90% confidence level.