We apply detailed observations of the color-magnitude relation (CMR) with the Advanced Camera for Surveys on the Hubble Space Telescope to study galaxy evolution in eight clusters at z 1. The early-type red sequence is well defined and elliptical and lenticular galaxies lie on similar CMRs. We analyze CMR parameters-scatter, slope, and zero point-as a function of redshift, galaxy properties and cluster mass. For bright galaxies (MB < -21 mag), the CMR scatter of the elliptical population in cluster cores is smaller than that of the S0 population, although the two become similar at faint magnitudes (MB > - 21 mag). While the bright S0 population consistently shows larger scatter than the ellipticals, the scatter of the latter increases in the peripheral cluster regions. If we interpret these results as due to age differences, bright elliptical galaxies in cluster cores are, on average, older than S0 galaxies and peripheral elliptical galaxies (by about 0.5 Gyr, using a simple, single-burst solar metallicity stellar population model). The CMR zero point, slope, and scatter in the (U - B) z = 0 rest-frame show no significant evolution out to redshift z 1.3 or significant dependence on cluster mass. Two of our clusters display CMR zero points that are redder (by 2 sigma ) than the average (U - B) z = 0 of our sample. We also analyze the fraction of morphological early-type and late-type galaxies on the red sequence. We find that, while in the majority of the clusters most (80% to 90%) of the CMR population is composed of early-type galaxies, in the highest-redshift, low-mass cluster of our sample, the CMR late-type/early-type fractions are similar (50%), with most of the late-type population composed of galaxies classified as S0/a. This trend is not correlated with the cluster's X-ray luminosity, or with its velocity dispersion, and could be a real evolution with redshift.