The green valley (GV) represents an important transitional state from actively star-forming galaxies to passively evolving systems. Its traditional definition, based on colour, rests on a number of assumptions that can be subjected to non-trivial systematics. In Angthopo, Ferreras & Silk (2019MNRAS.488L..99A), we proposed a new definition of the GV based on the 4000{AA} break strength. In this paper, we explore in detail the properties of the underlying stellar populations by use of ~230 thousand high-quality spectra from the Sloan Digital Sky Survey (SDSS), contrasting our results with a traditional approach via dust-corrected colours. We explore high-quality stacked SDSS spectra, and find a population trend that suggests a substantial difference between low- and high-mass galaxies, with the former featuring younger populations with star formation quenching, and the latter showing older (post-quenching) populations that include rejuvenation events. Subtle but measurable differences are found between a colour-based approach and our definition, especially as our selection of GV galaxies produces a cleaner 'stratification' of the GV, with more homogeneous population properties within sections of the GV. Our definition based on 4000{AA} break strength gives a clean representation of the transition to quiescence, easily measurable in the upcoming and future spectroscopic surveys.