Computer simulations are invaluable for the study of ultrafast phenomena, as they allow us to directly access the electron dynamics. We present an efficient method for simulating the evolution of electrons in molecules under the influence of time-dependent electric fields, based on the Gaussian tight binding model. This model improves upon standard self-charge-consistent tight binding by the inclusion of polarizable orbitals and a self-consistent description of charge multipoles. Using the examples of bithiophene, terthiophene, and tetrathiophene, we show that this model produces electrostatic, electrodynamic, and explicitly time-dependent properties in strong agreement with density-functional theory, but at a small fraction of the cost.