This paper addresses the challenge of understanding the typical star formation histories of red sequence galaxies, using linestrength indices and mass-to-light ratios as complementary constraints on their stellar age distribution. We construct simple parametric models of the star formation history that bracket a range of scenarios, and fit these models to the linestrength indices of low-redshift cluster red-sequence galaxies. For giant galaxies, we confirm the downsizing trend. We find, however, that this trend flattens or reverses at sigma < 70 km/s. We then compare predicted stellar mass-to-light ratios with dynamical mass-to-light ratios derived from the Fundamental Plane (FP), or by the SAURON group. For galaxies with sigma ~ 70 km/s, models with a frosting of young stars and models with exponential star formation histories have stellar mass-to-light ratios that are larger than observed dynamical mass-to-light ratios by factors of 1.7 and 1.4, respectively, and so are rejected. The SSP model is consistent with the FP, and requires a modest amount of dark matter (20-30%) to account for the difference between stellar and dynamical mass-to-light ratios. A model in which star formation was quenched at intermediate ages is also consistent with the observations. We find that the contribution of stellar populations to the tilt of the FP is highly dependent on the assumed star-formation history: for the SSP model, the tilt of the FP is driven primarily by stellar-population effects. For a quenched model, two-thirds of the tilt is due to stellar populations and only one third is due to dark matter or non-homology.
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