Time-resolved spontaneous and laser-induced unimolecular fragmentation of perylene cations (C20H12+) has been measured on timescales up to 2 s in a cryogenic electrostatic ion beam storage ring. We elaborate a quantitative model, which includes fragmentation in competition with radiative cooling via both vibrational and electronic (recurrent fluorescence) de-excitation. Excellent agreement with experimental results is found when sequential fragmentation of daughter ions co-stored with the parent perylene ions is included in the model. Based on the comparison of the model to experiment, we constrain the oscillator strength of the D-1 -> D-0 emissive electronic transition in perylene (f(RF) = 0.055 +/- 0.011), as well as the absolute absorption cross section of the D-5 <- D-0 excitation transition (sigma (abs) > 670 Mb). The former transition is responsible for the laser-induced and recurrent fluorescence of perylene, and the latter is the most prominent in the absorption spectrum. The vibrational cooling rate is found to be consistent with the simple harmonic cascade approximation. Quantitative experimental benchmarks of unimolecular processes in polycyclic aromatic hydrocarbon ions like perylene are important for refining astrochemical models.