  Vela X-1 is the archetypical eclipsing high-mass X-ray binary, composed of a
neutron star (NS) accreting the B-star wind. It was observed by nearly all
X-ray observatories, often multiple times, featuring a rich spectrum of
variable emission lines. Yet, the precise origin of these lines in the binary
system remains uncertain. We perform a systematic, orbital phase-dependent
analysis of the reflected Fe K$\alpha$ fluorescence line at 6.4 keV using over
100 NICER observations. We resolve the line variability into 500s time bins and
find that it is predominantly due to variation in the ionizing flux, with a
moderate underlying phase dependence over the 9-day orbital period. Our
analysis reveals a significant reflection component that cannot originate from
the companion B-star alone. We also find that an appreciable portion of the
B-star surface is obscured opposite the eclipse, and this obscuration is not
symmetric around the mid-point (phase=0.5). We argue that an accretion stream,
from the B-star to the NS and distorted by the orbital motion, is responsible
for both the additional fluorescence emission component and for obscuring the
B-star.
