Nanoparticle-on-mirror (NPoM) configurations have demonstrated enormous enhancements toward Raman scattering due to a highly confined and amplified electromagnetic field within the nano/picocavity between the gold nanoparticle and the underlying ultrasmooth gold film. While the dipolar gap mode has been often referred to in view of its high Raman enhancement, we contend that higher order plasmonic modes such as the quadrupole mode can contribute significantly at the commonly used Raman exciting wavelength of around 633 nm. This finding is supported by experimental results obtained by exciting the NPoM configuration in the focus of a linearly, radially, and azimuthally polarized laser. We demonstrate that both in-plane and out-ofplane electric fields are suitable for enhancing the Raman scattering of Rhodamine 6G (R6G) molecules sandwiched in the NPoM configuration making use of the field distribution of the higher order gap mode, as confirmed by boundary element method simulations. Further, significant variations in the polarization-dependent optical response can be seen for the investigated individual NPoMs, which are attributed to variations in the individual NPoM geometries. As the probe molecule for our studies is Rhodamine 6G (R6G), Raman spectra show peak-specific enhancement factors, which correlate with the tensor properties of individual vibrational modes.