Haven’t been able to record it yet, but the sound only happens when the power supply is plugged into the HDD and the outlet (not one or the other), and the HDD is NOT plugged into the computer.
Plugging the HDD into the computer stops the sound. I was unplugging it from the PC to keep it offline when I didn’t need it. (After safely ejecting and waiting etc. of course)
I guess I’ll just need to unplug the power when I’m not using it, too.