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 type 3 promoter by SNAP-type and TFIIIC-type factors, binds to DNA, recruits RNA polymerase III and facilitates the transition from the closed to the open complex.