Total solar eclipses (TSEs) provide a unique opportunity to quantify the properties of the K-corona (electrons), F-corona (dust) and E-corona (ions) continuously from the solar surface out to a few solar radii. We apply a novel inversion method to separate emission from the K- and F-corona continua using unpolarized total brightness (tB) observations from five 0.5 nm bandpasses acquired during the 2019 July 2 TSE between 529.5 nm and 788.4 nm. The wavelength dependence relative to the photosphere (i.e., color) of the F-corona itself is used to infer the tB of the K- and F-corona for each line-of-sight. We compare our K-corona emission results with the Mauna Loa Solar Observatory (MLSO) K-Cor polarized brightness (pB) observations from the day of the eclipse, and the forward modeled K-corona intensity from the Predictive Science Inc. (PSI) Magnetohydrodynamic (MHD) model prediction. Our results are generally consistent with previous work and match both the MLSO data and PSI-MHD predictions quite well, supporting the validity of our approach and of the PSI-MHD model. However, we find that the tB of the F-corona is higher than expected in the low corona, perhaps indicating that the F-corona is slightly polarized -- challenging the common assumption that the F-corona is entirely unpolarized.