We use 250 radio loud quasars with UBV photometry available and z < 1.65, to study whether there is a gap in the distribution of absolute magnitudes, from M-V approximate to -25.8 (for H-o = 100 kms(-1) Mpc(-1), q(0) = 0.5) to -25.3, as was suggested by Teerikorpi (1981b; Paper I). In Paper I it was also proposed that there is a class of the most luminous radio quasars, differing in some properties from fainter quasars on the other side of the gap. The main conclusion of Paper I remains intact. The gap in the distribution of absolute magnitudes is confirmed with the new formalism of cosmological Malmquist bias (Teerikorpi 1998), which allows one to use heterogeneous samples with magnitude inhomogeneity. Comparison of optical variability and polarization of quasars on either side of the gap supports the conclusion in Paper I that the gap separates quasars with differing properties, with a tentative class "AI" around M-V approximate to -26.0 (or -27.5 for H-0 = 50). AI quasars are less variable than fainter quasars just beyond the gap, as already suggested in Paper I. Also, optical polarization of AI's is low, typically less than I percent, while beyond the gap one finds higher polarizations, mostly between 1 and 10 percent. That the AI population is rare below z approximate to 0.5 may relate to the observation that low-redshift quasars and radio galaxies avoid rich clusters. For z < 0.5 the variability of the fainter ones is similar to the AI with z > 0.5. For z > 0.5 the optical activity starts to increase. Optical polarization behaves in an analogous manner. The evidence justifies further studies of the quasars in the AI absolute magnitude domain and its vicinity, including analysis of their radio properties and high resolution imaging of their hosts and environments at these intermediate redshifts (Papers III-IV). As the AI + the gap may be related to a phase of galaxy clustering, it is important to know at how high redshifts it is already present.