  Recent observations have discovered long (up to ~110 Mpc/h), opaque
Gunn-Peterson troughs in the z ~ 5.5 Lyman-alpha forest, which are challenging
to explain with conventional models of the post-reionization intergalactic
medium. Here we demonstrate that observations of the galaxy populations in the
vicinity of the deepest troughs can distinguish two competing models for these
features: deep voids where the ionizing background is weak due to fluctuations
in the mean free path of ionizing photons would show a deficit of galaxies,
while residual temperature variations from extended, inhomogeneous reionization
would show an overdensity of galaxies. We use large (~550 Mpc/h) semi-numerical
simulations of these competing explanations to predict the galaxy populations
in the largest of the known troughs at z ~ 5.7. We quantify the strong
correlation of Lyman-alpha effective optical depth and galaxy surface density
in both models and estimate the degree to which realistic surveys can measure
such a correlation. While a spectroscopic galaxy survey is ideal, we also show
that a relatively inexpensive narrowband survey of Lyman-alpha-emitting
galaxies is ~90% likely to distinguish between the competing models.
