Well, the whine is gone. I don't know for sure what it was, but I altered the angle of my windshield to just a smidge more vertical and the noise went away. It must have been some sort of resonance caused by the air passing between the w/s and the speedo. By tilting the w/s up a hair more the gap between the 2 is ever-so-slightly reduced, and now the "hearing test" noises are gone.
Thanks to all for the input and suggestions.
