One thing to keep in mind when you are in "auto" 4WD.
The way I understand that it works is that the front hubs get locked, and the front drive shaft clutch in the transfer case is normally disengaged. Then, when slippage is detected, the transfer case clutch engages to give you four wheel drive.
What this means is that when you are in auto, the front drive shafts, differential, and drive shaft back to the transfer case are always spinning, even if the transfer case clutch is not sending it power.
I have noticed at times that when I am in auto, I will sometimes notice a little gear noise, especially when cornering. I don't so much as hear it as I feel an almost imperceptable vibration or growl in the steering wheel and my feet. I've pointed it out to my wife when it happens, and she can neither hear nor feel anything. She thinks I'm nuts. (She's probably right!)
I'm chalking this up to the fact that you are spinning these shafts and diff gears without any load on them, and there is just a slight amount of backlash and gear noise in them. I don't think that it's a problem. It's similar to, but less than, the additional gear noise/vibration when in 4Hi.
I would not call this sensation a whine, grind, click, or thump, but I could go along with ultravorx's description of a low harmonic hum. Generally lasts for less than a second at a time.
Could this be what you are experiencing?