Interacting selectively and non-covalently with an RNA polymerase III (Pol III) complex, typically composed of seventeen subunits, and with another protein, macromolecule, or complex, permitting those molecules to function in a coordinated way, Once recruited to an RNA polymerase III promoter by one or more other transcription factors, binds to DNA, recruits RNA polymerase III and facilitates the transition from the closed to the open complex.