  Since the photons that stream from QSOs alter the ionization state of the gas
they traverse, any changes to a QSO's luminosity will produce
outward-propagating ionization gradients in the surrounding intergalactic gas.
This paper shows that at redshift z~3 the gradients will alter the gas's
Lyman-alpha absorption opacity enough to produce a detectable signature in the
spectra of faint background galaxies. By obtaining noisy (S:N~4) low-resolution
(~7A) spectra of a several dozen background galaxies in an R~20' field
surrounding an isotropically radiating 18th magnitude QSO at z=3, it should be
possible to detect any order-of-magnitude changes to the QSO's luminosity over
the previous 50--100 Myr and to measure the time t_Q since the onset of the
QSO's current luminous outburst with an accuracy of ~5 Myr for t_Q<~50 Myr.
Smaller fields-of-view are acceptable for shorter QSO lifetimes. The major
uncertainty, aside from cosmic variance, will be the shape and orientation of
the QSO's ionization cone. This can be determined from the data if the number
of background sources is increased by a factor of a few. The method will then
provide a direct test of unification models for AGN.
