  Using a magnitude-limited, spectroscopic survey of the X-ray luminous galaxy
cluster MS1054-03, we isolate 153 cluster galaxies and measure MS1054's
redshift and velocity dispersion to be z=0.8307 and sigma_z=1156 km/s. The
absorption-line, post-starburst (``E+A''), and emission-line galaxies
respectively make up 63%, 15%, and 23% of the cluster population. With
photometry from HST/ACS, we find that the absorption-line members define an
exceptionally tight red sequence over a span of ~3.5 magnitudes in i775: their
intrinsic scatter in (V-i) color is only 0.048, corresponding to a (U-B)_z
scatter of 0.041. Their color scatter is comparable to that of the ellipticals
(sigma_Vi=0.055), but measurably smaller than that of the combined E+S0 sample
(sigma_Vi=0.072). The color scatter of MS1054's absorption-line population is
approximately twice that of the ellipticals in Coma; this difference is
consistent with passive evolution where most of the absorption-line members
(>75%) formed by z~2, and all of them by z~1.2. For red members, we find a
trend (>95% confidence) of weakening Hdelta absorption with redder colors that
we conclude is due to age: in MS1054, the color scatter on the red sequence is
driven by differences in mean stellar age of up to ~1.5 Gyr. We also generate
composite spectra and estimate that the average S0 in MS1054 is ~0.5-1 Gyr
younger than the average elliptical; this difference in mean stellar age is
mainly due to a number of S0s that are blue (18%) and/or are post-starburst
systems (21%).
