  We show that comparisons of HeII Lyman-alpha forest lines of sight to nearby
quasar populations can strongly constrain the lifetimes and emission geometry
of quasars. By comparing the HeII and HI Lyman-alpha forests along a particular
line of sight, one can trace fluctuations in the hardness of the radiation
field (which are driven by fluctuations in the HeII ionization rate). Because
this high-energy background is highly variable - thanks to the rarity of the
bright quasars that dominate it and the relatively short attenuation lengths of
these photons - it is straightforward to associate features in the radiation
field with their source quasars. Here we quantify how finite lifetimes and
beamed emission geometries affect these expectations. Finite lifetimes induce a
time delay that displaces the observed radiation peak relative to the quasar.
For beamed emission, geometry dictates that sources invisible to the observer
can still create a peak in the radiation field. We show that both these models
produce substantial populations of "bare" peaks (without an associated quasar)
for reasonable parameter values (lifetimes ~10^6-10^8 yr and beaming angles <90
degrees). A comparison to existing quasar surveys along two HeII Lyman-alpha
forest lines of sight rules out isotropic emission and infinite lifetime at
high confidence; they can be accommodated either by moderate beaming or
lifetimes ~10^7-10^8 yr. We also show that the distribution of radial
displacements between peaks and their quasars can unambiguously distinguish
these two models, although larger statistical samples are needed.
