Thank you Petehouk!
Well whaddya know, it is a little fan back there making the noise. I pulled it out and it was filthy dirty. Greasy lint all over the impeller, and very dusty. Took it apart and cleaned it up with q-tip swabs, alcohol, and compressed air. There is a little thermistor and humidity sensor on the internal circuit board. But after installing, it still made the noise. So at least I know the cause of the noise, but I wonder if a new part would be just as noisy? The fan motor design reminded me of a stepper motor, but spinning the impeller did not have a cogging feeling.
Here it is at Rock Auto. $46
https://www.rockauto.com/en/moreinfo.php?pk=4332603&cc=3436086&pt=14376&jsn=478
Ebay $25 pre-owned
https://www.ebay.com/itm/134024736256 Probably no better than the one in your car right now.
China knock-off, if you would believe it, at Amazon $30
https://www.amazon.com/Sumyola-Outdoor-Temperature-BM5T-8B506-AB-19C734/dp/B0CN4DGPXG The original equipment seems cheaply made, so this knock off is probably total thit.
To Remove
1. Raise the steering wheel to the highest position.
2. Reach your left hand into the opening under the steering column, and move your fingers to the right, towards the nickel-sized round vent. If you have big hands, you may not be able to do this.
3. The fan is press fit to the backside of the lower instrument panel trim at that vent. Just move the fan towards the front of the car to pull it out of the trim.
4 Bring the fan out through the opening under the steering column.
5. Disconnect the harness from the fan connector, by moving the tab on the connector away from the harness.
Installation is the reverse.