We present the results of a deep narrowband [O II] ?3727 emission line search for faint (g < 27), star-forming galaxies in the field of the z = 0.37 MS 1512.4+3647 cluster. We find no evidence for an overdensity of emission-line sources relative to the field at z ~ 0.4 and therefore conclude that the MS 1512.4+3647 sample is dominated by field [O II] emission line galaxies that lie along the ~180 Mpc line of sight immediately in front of and behind the cluster. This is surprising, given that the previously surveyed z = 0.41 cluster A851 has 3-4 times the field emission-line galaxy density. We find that the MS 1512.4+3647 sample is deficient in galaxies with intermediate colors (1.0 < g-i < 2.0) and implied star formation exponential decay timescales ? ~ 100 Myr-1 Gyr that dominate the A851 emission-line galaxy population. Instead, the majority of [O II] emission line galaxies surrounding the MS 1512.4+3647 cluster are blue (g-i ? 1.0) and forming stars in bursts with ? < 100 Myr. In both samples, galaxies with the shortest star formation timescales are preferentially among the faintest star-forming objects. Their i luminosities are consistent with young stellar populations ~108-109 M?, although an additional factor of 10 in stellar mass could be hiding in underlying old stellar populations. We discuss the implications for the star formation histories of dwarf galaxies in the field and rich clusters.