Atomically-sharp tips in close proximity of metal surfaces create plasmonic nanocavities supporting both radiative (bright) and non-radiative (dark) localized surface plasmon modes. Disentangling their respective contributions to the total density of optical states remains a challenge. Electroluminescence due to tunnelling through the tip-substrate gap could allow the identification of the radiative component, but this information is inherently convoluted with that of the electronic structure of the system. In this work, we present a fully experimental procedure to eliminate the electronic-structure factors from the scanning tunnelling microscope luminescence spectra by confronting them with spectroscopic information extracted from elastic current measurements. Comparison against electromagnetic calculations demonstrates that this procedure allows the characterization of the meV shifts experienced by the nanocavity plasmonic modes under atomic-scale gap size changes. Therefore, the method gives access to the frequency-dependent radiative Purcell enhancement that a microscopic light emitter would undergo when placed at such nanocavity.