Dash Noise Getting Louder w/ Speed - Help

[2001 TX Tahoe]

2001 Tahoe, just hit 200K miles a few weeks ago. One day I had a new noise which sounds like it's coming from behind the driver's side dash, kind of the instrument panel area and it hasn't gone away. It gets louder with speed (not RPMs) and isn't audible below 10 mph. It's kind of like a buzzing/whirring/grinding noise. It sounds mechanical. It does the same thing whether or not my A/C is turned on or turned off. All gauges appear to be working. A/C is working. Any ideas?
Thanks,
DC

 

[2001 TX Tahoe]

So I just tried a few things while driving while it was making the sound. Changed the A/C from off to on, hot to cold, dash vents to floor vents, recirculate on and off, and this didn't change anything. Shifting into Auto 4wd, 4H, and 2wd. No change. Then pulled the column shifter toward me as if to change gears and the tone of the noise changed and I could feel it in the shifter. I was able to downshift and upshift, but each time I could feel a slight vibration in the shifter and the tone would slightly change when I shifted gears. Ideas??