We present new absorption-line analysis and new galaxy survey data obtained for the field around PKS 0405-123 at z_QSO_=0.57. Combining previously known OVI absorbers with new identifications in the higher S/N ultraviolet (UV) spectra obtained with the Cosmic Origins Spectrograph, we have established a sample of 7 OVI absorbers and 12 individual components at z=0.0918-0.495 along the sightline towards PKS 0405-123. We complement the available UV absorption spectra with galaxy survey data that reach 100 percent completeness at projected distances {rho}<200kpc of the quasar sightline for galaxies as faint as 0.1L* (0.2L*) out to redshifts of z~0.35 (z~0.5). The high level of completeness achieved at faint magnitudes by our survey reveals that OVI absorbers are closely associated with gas-rich environments containing at least one low-mass, emission-line galaxy. An intriguing exception is a strong OVI system at z~0.183 that does not have a galaxy found at {rho}<4Mpc, and our survey rules out the presence of any galaxies of L>0.04L* at {rho}<250kpc and any galaxies of L>0.3L* at {rho}<1Mpc. We further examine the galactic environments of OVI absorbers and those 'Ly{alpha}-only' absorbers with neutral hydrogen column density log N(HI)<13.6 and no detectable OVI absorption features. The Ly{alpha}-only absorbers serve as a control sample in seeking the discriminating galactic features that result in the observed Ovi absorbing gas at large galactic radii. We find a clear distinction in the radial profiles of mean galaxy surface brightness around different absorbers. Specifically, Ovi absorbers are found to reside in regions of higher mean surface brightness at {rho}<~500kpc ({Delta}{mu}_R_~+5magMpc^-2^ relative to the background at {rho}>500kpc), while only a mild increase in galaxy surface brightness is seen at small {rho} around Ly{alpha}-only absorbers ({Delta}{mu}_R_~+2magMpc^-2^). The additional insights gained from our deep galaxy survey demonstrate the need to probe the galaxy populations to low luminosities in order to better understand the nature of the absorbing systems.