Theory predicts that a strongly injection-locked spin-torque oscillator (STO) should show a characteristic ringing frequency both on its approach to the locked state and under the influence of thermal noise. While experiments have so far failed to detect such ringing, we here show numerically and analytically how current modulation of injection-locked STOs can excite the ringing frequency in a resonant manner, and hence increase the experimental sensitivity. The complexity of such dynamics leads to a nonlinear resonance, which can even unlock the STO as a function of the modulation strength. The results presented here offer a plausible method for experimentally measuring the ringing frequency of STOs. Moreover, the onset of unlocking also provides a measure for the maximum modulation strength that can be applied to phase-locked STOs.