I picked up a stethoscope some time ago when I was trying to diagnose a pulley bearing issue on another car, and I took it out to the BRZ. I hunted around that side of the car until I came upon this spot with the probe:
The chirp at this point finally came into the earpieces of the stethoscope and was matched with the low-frequency tapping I had heard while touching the probe to the other metal parts in that area.
It sounds like the chirp is the result of the insulation and metal components in the DI pump area acting like a high-pass filter, so that we only hear the highest pitch of the tapping.
I am not a skilled diagnostician, so take this with a grain of salt. Maybe someone with better ears will go poke around in this specific area.