Lightwave electronics offer transformative field-level precision and control at high optical frequencies. While recent advances show that lightwave-driven electron emission from nanoantennas enables time-domain, field-resolved analysis of optical waveforms through a small-signal analysis, the effect of the gate waveform on the measurement transfer function remains unexplored. By generating electrons with a 10-cycle pulse in the optical tunneling regime and perturbing the response with a 1.5-cycle pulse, we experimentally measure the bandwidth limitations imposed by the electron emission process. By comparing these measurements with TDSE simulations and analytical models, we reveal the temporal properties of the electronic response and its impact on the small-signal transfer function. Our results test and confirm the accuracy of the Fowler–Nordheim model in estimating the lightwave electronic response from noble metals. We envision extending these techniques to multi-octave-spanning signals for precise characterization of sub-cycle electronic responses through harmonic frequency mixing.