The collisionless plasma of the Versatile Toroidal Facility experiment [J. Egedal, A. Fasoli, M. Porkolab, and D. Tarkowski, Rev. Sci. Instrum. 71, 3351 (2000)], applied to the study of magnetic reconnection, exhibits a global eigenmode response during which the reconnection rate and the current channel oscillate. The present paper describes experiments tailored for investigating this eigenmode response. It is found that the oscillatory plasma behavior is linked to ion-polarization currents and associated electron currents that flow to maintain quasineutrality within the active reconnection region. A theoretical model is developed which describes the eigenmode response and accounts for the temporal evolution of the measured profiles of key plasma parameters. (c) 2005 American Institute of Physics.