  The transmission of Lyman-{\alpha} (Ly{\alpha}) in the spectra of distant
quasars depends on the density, temperature, and ionization state of the
intergalactic medium (IGM). Therefore, high-redshift (z > 5) Ly{\alpha} forests
could be invaluable in studying the late stages of the epoch of reionization
(EoR), as well as properties of the sources that drive it. Indeed, high-quality
quasar spectra have now firmly established the existence of large-scale opacity
fluctuations at z > 5, whose physical origins are still debated. Here we
introduce a Bayesian framework capable of constraining the EoR and galaxy
properties by forward-modelling the high-z Ly{\alpha} forest. Using priors from
galaxy and CMB observations, we demonstrate that the final overlap stages of
the EoR (when >95% of the volume was ionized) should occur at z < 5.6, in order
to reproduce the large-scale opacity fluctuations seen in forest spectra.
However, it is the combination of patchy reionization and the inhomogeneous UV
background that produces the longest Gunn-Peterson troughs. Ly{\alpha} forest
observations tighten existing constraints on the characteristic ionizing escape
fraction of galaxies, with the combined observations suggesting f_{\rm esc}
\approx 7^4_3%, and disfavoring a strong evolution with the galaxy's halo (or
stellar) mass.
