We consider a family of totally asymmetric simple exclusion processes (TASEPs), consisting of particles on a lattice that require binding by a "token" in various physical configurations to advance over the lattice. Using a combination of theory and simulations, we address the following questions: (i) How token binding kinetics affects the current-density relation on the lattice; (ii) How this current-density relation depends on the scarcity of tokens; (iii) How tokens propagate the effects of the locally-imposed disorder (such as a slow site) over the entire lattice; (iv) How a shared pool of tokens couples concurrent TASEPs running on multiple lattices; (v) How our results translate to TASEPs with open boundaries that exchange particles with the reservoir. Since real particle motion (including in biological systems that inspired the standard TASEP model, e.g., protein synthesis or movement of molecular motors) is often catalyzed, regulated, actuated, or otherwise mediated, the token-driven TASEP dynamics analyzed in this paper should allow for a better understanding of real systems and enable a closer match between TASEP theory and experimental observations.