Galaxy evolution in the post-merger regime. II -- Post-merger quenching peaks within 500 Myr of coalescence

(Abridged) Mechanisms for quenching star formation in galaxies remain hotly debated, with galaxy mergers an oft-proposed pathway. In Ellison et al. (2022) we tested this scenario by quantifying the fraction of recently and rapidly quenched post-starbursts (PSBs) in a sample of post-merger galaxies identified in the Ultraviolet Near Infrared Optical Northern Survey (UNIONS). With our recent development of the Multi-Model Merger Identifier (MUMMI) neural network ensemble (Ferreira et al. 2024a,b), we are now additionally able to predict the time since coalescence (T_PM) for the UNIONS post-merger galaxies up to T_PM = 1.8 Gyr, allowing us to further dissect the merger sequence and measure more precisely when quenching occurs. Based on a sample of 5927 z<0.3 post-mergers identified in UNIONS, we find that the post-coalescence population evolves from one dominated by star-forming (and starbursting) galaxies at 0 < T_PM < 0.16 Gyr, through to a population that is dominated by quenched galaxies by T_PM ~ 1.5 Gyr. We find a PSB excess throughout the post-merger regime, but with a clear peak at 0.16 < T_PM < 0.48 Gyr. In this post-merger time range PSBs are more common than in control galaxies by factors of 30-100, an excess that drops sharply at longer times since merger. We also quantify the fraction of PSBs that are mergers and find that the majority (75%) of classically selected E+A are identified as mergers, with a lower merger fraction (60%) amongst PCA selected PSBs. Our results demonstrate that 1) galaxy-galaxy interactions can lead to rapid post-merger quenching within 0.5 Gyr of coalescence, 2) the majority of (but not all) PSBs at low z are linked to mergers and 3) quenching pathways are diverse, with different PSB selection techniques likely identifying galaxies quenched by different physical processes with an additional dependence on stellar mass.