Singlet fission is an excitation multiplication process in molecular systems that can circumvent energy losses and significantly boost solar cell efficiencies; however, the nature of a critical intermediate that enables singlet fission and details of its evolution into multiple product excitations remain obscure. We resolve the initial sequence of events comprising the fission of a singlet exciton in solids of pentacene derivatives using femtosecond transient absorption spectroscopy. We propose a three-step model of singlet fission that includes two triplet-pair intermediates and show how transient spectroscopy can distinguish initially interacting triplet pairs from those that are spatially separated and noninteracting. We find that the interconversion of these two triplet-pair intermediates is limited by the rate of triplet transfer. These results clearly highlight the classical kinetic model of singlet fission and expose subtle details that promise to aid in resolving problems associated with triplet extraction.