In this research, we investigated the dependence of the saturation-induced gain modulation (SIGM) on the modulation frequency of the input signal in an erbium-doped fiber amplifier (EDFA). By finding and incorporating the modulation frequency invariance of the SIGM realizable within some frequency range, we demonstrated a repetition-rate-selectable high-speed optical gating in two-terminal electrical devices based on vanadium-dioxide thin films. In the implemented optical gating system, the repetition rate could be freely chosen as an arbitrary frequency between 0.27 and 10 kHz without any degradation of the gating speed and the signal-to-noise ratio.