In my car, the noise turned out to be coming from the steering column, which had developed a slight amount of play over time.
Over time, the steering of my '91 started sounding a bit loose and rattly when driving over bumps. I could duplicate the noise when the car was standing still by turning the steering wheel back and forth about an inch really quickly.
My dealer first told me the tie rods were shot, so I had those replaced. The noise was still there and my dealer then diagnosed the steering rack as the culprit. Unfortunately, adjusting and then replacing the steering rack didn't get rid of the noise either. I decided to investigate myself since my confidence in my dealer was falling quickly. Laying in the car with my head by the petals and turning the steering column back and forth, I could hear that the noise wasn't coming from the U-joints that connect the steering column to the steering rack, even though noise from those joints is supposedly not uncommon. Rather, the noise came from further up, from somewhere inside the steering column. I bought a used column on NSX Prime that didn't have any play and after installing it in my car, the noise is gone.