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Understanding the late-stage evolution of the most massive stars such as$\eta$ Carinae is challenging because no true analogs of $\eta$ Car have beenclearly identified in the Milky Way or other galaxies. In Khan et. al. (2013),we utilized Spitzer IRAC images of $7$ nearby ($\lesssim4$ Mpc) galaxies tosearch for such analogs, and found $34$ candidates with flat or red mid-IRspectral energy distributions. Here, in Paper II, we present ourcharacterization of these candidates using multi-wavelength data from theoptical through the far-IR. Our search detected no true analogs of $\eta$ Car,which implies an eruption rate that is a fraction $0.01\lesssim F \lesssim0.19$ of the ccSN rate. This is roughly consistent with each $M_{ZAMS} \gtrsim70M_\odot$ star undergoing $1$ or $2$ outbursts in its lifetime. However, we doidentify a significant population of $18$ lower luminosity$\left(\log(L/L_\odot)\simeq5.5-6.0\right)$ dusty stars. Stars enter this phaseat a rate that is fraction $0.09 \lesssim F \lesssim 0.55$ of the ccSN rate,and this is consistent with all $25 < M_{ZAMS} < 60M_\odot$ stars undergoing anobscured phase at most lasting a few thousand years once or twice. These phasesconstitute a negligible fraction of post-main sequence lifetimes of massivestars, which implies that these events are likely to be associated with specialperiods in the evolution of the stars. The mass of the obscuring material is oforder $\sim M_\odot$, and we simply do not find enough heavily obscured starsfor theses phases to represent more than a modest fraction ($\sim 10\%$ not$\sim 50\%$) of the total mass lost by these stars. In the long term, thesources that we identified will be prime candidates for detailed physicalanalysis with JWST.

Finding $\eta$ Car Analogs in Nearby Galaxies Using Spitzer: II. Identification of An Emerging Class of Extragalactic Self-Obscured Stars