The usage of computationally feasible overparametrized and nonregularized system identification signal processing methods is assessed for automated determination of the full reversed-field pinch external plasma response spectrum for the experiment EXTRAP T2R. No assumptions on the geometry of eigenmodes are imposed. The attempted approach consists of high-order autoregressive exogenous estimation followed by Markov block coefficient construction and Hankel matrix singular value decomposition. It is seen that the obtained 'black-box' state-space models indeed can be compared with the commonplace ideal magnetohydrodynamics (MHD) resistive thin-shell model in cylindrical geometry. It is possible to directly map the most unstable autodetected empirical system pole to the corresponding theoretical resistive shell MHD eigenmode.