The triplet to triplet absorption spectrum of pyrene, first measured by Craig and Ross, underpins technological applications and has been measured many times, focusing mostly on two intense transitions spanning from the green to the UV regions. Nevertheless, there has been little attention paid to its very weak IR absorption and its weak absorption in the red, even though the IR band reveals information critical to many practical applications. Holistically, a critical work is the 1970 extensive spectral measurement and assignment of Langelaar et al. Using calculations of very different types (the CAM-B3LYP density-functional, coupled-cluster, and complete active space self-consistent field (CASSCF) approaches), we vindicate their assignment of four Franck-Condon spectra progressions. Three new region embodying unaccounted absorption are also identified, leading to the characterization of an additional dark state. Across the whole spectrum, strong vibronic coupling is predicted to lead to Herzberg-Teller effects that account for the unassigned absorptions to drive non-adiabatic couplings that would provide for very rapid energy relaxation, withing the triplet manifold, to the lowest-energy triplet excited state T2 of symmetry 3B2g. Evidence is also obtained indicating the presence of low-lying conical intersections involving the next two triplet states, (1)3B2u and (1)3Ag.