To clarify the physical nature of the enigmatic scattering polarization in the Na i D$_1$ and D$_2$ line cores we have explored their behavior with full Stokes vector polarimetry in regions with varying degree of magnetic activity near the solar limb. These observations represent the first time that ZIMPOL II, the second generation of our CCD based imaging polarimeter systems, has been used for a scientific program. With ZIMPOL II the four Stokes images can be demodulated and recorded with a single CCD sensor such that the resulting images of the fractional polarization Q/I, U/I, and V/I are entirely free from spurious features due to seeing or flat-field effects. The polarization in the cores of the lines, in particular in D$_2$, exhibits dramatic and unexpected spatial variations in both Q/I and U/I, including polarization self-reversals of the D$_2$ Q/I core peak. As the fluctuations in the Q, U, and V parameters appear to be relatively uncorrelated, we have parametrized the profiles and made scatter plots of the extracted parameters. Comparison with synthetic scatter plots based on different theoretical models suggests that the polarization signals in the cores of the D$_2$ and D$_1$ lines have different physical origins: While the D$_1$ core is likely to be governed by ground-state atomic polarization, the D$_2$ core is dominated by the alignment of the excited state and by effects of partial frequency redistribution.