  We report the discovery of the faint (V=21.7) quasar QSO03027-0010 at z=2.808
in the vicinity of Q0302-003, one of the few quasars observed with STIS to
study intergalactic HeII absorption. Together with another newly discovered QSO
at z=2.29, there are now 6 QSOs known near the line of sight towards Q0302-003,
of which 4 are located within the redshift region 2.76<=z<=3.28 covered by the
STIS spectrum. We correlated the opacity variations in the HI and HeII Lyman
forest spectra with the locations of known quasars. There is no significant
proximity effect in the HI Lyman alpha forest for any of the QSOs, except for
the well-known line of sight effect for Q0302-003 itself. By comparing the
absorption properties in HI and HeII, we estimated the fluctuating hardness of
the extragalactic UV radiation field along this line of sight. We find that
close to each foreground quasar, the ionizing background is considerably harder
than on average. In particular, our newly discovered QSO03027-0010 shows such a
hardness increase despite being associated with an overdensity in the HI Lyman
forest. We argue that the spectral hardness is a sensitive physical measure to
reveal the influence of QSOs onto the UV background even over scales of several
Mpc, and that it breaks the density degeneracy hampering the traditional
transverse proximity effect analysis. We infer from our sample that there is no
need for significantly anisotropic UV radiation from the QSOs. From the
transverse proximity effect detected in the sample we obtain minimum quasar
lifetimes in the range ~10-30 Myr.
