Controllable topological phase transitions in low dimensional materials allows for unconventional optical selection rules and exciton series. We show that the broad mixing of single-particle contributions to the exciton states occurring across a Z2 phase transition in 1D polyacene polymers leads to an extreme tunability of optical properties, with exciton dispersions ranging from gigantic bandwidth (≈ 1.5 eV) to practically zero. The acene length transversal to the periodic axis controls the exciton localization, allowing for a cross-over from Mott-Wannier to Frenkel-like excitons and large changes in optical gaps, singlet-triplet splittings and the orbital structure of the real-space exciton states. Our work opens appealing perspectives for the design of novel optolectronic devices.