  Understanding the late-stage evolution of the most massive stars such as
$\eta$ Carinae is challenging because no true analogs of $\eta$ Car have been
clearly identified in the Milky Way or other galaxies. In Khan et. al. (2013),
we utilized Spitzer IRAC images of $7$ nearby ($\lesssim4$ Mpc) galaxies to
search for such analogs, and found $34$ candidates with flat or red mid-IR
spectral energy distributions. Here, in Paper II, we present our
characterization of these candidates using multi-wavelength data from the
optical through the far-IR. Our search detected no true analogs of $\eta$ Car,
which implies an eruption rate that is a fraction $0.01\lesssim F \lesssim
0.19$ of the ccSN rate. This is roughly consistent with each $M_{ZAMS} \gtrsim
70M_\odot$ star undergoing $1$ or $2$ outbursts in its lifetime. However, we do
identify a significant population of $18$ lower luminosity
$\left(\log(L/L_\odot)\simeq5.5-6.0\right)$ dusty stars. Stars enter this phase
at 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 an
obscured phase at most lasting a few thousand years once or twice. These phases
constitute a negligible fraction of post-main sequence lifetimes of massive
stars, which implies that these events are likely to be associated with special
periods in the evolution of the stars. The mass of the obscuring material is of
order $\sim M_\odot$, and we simply do not find enough heavily obscured stars
for 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, the
sources that we identified will be prime candidates for detailed physical
analysis with JWST.
