Update on my truck.
I took it to the dealership, had them check it out. The transmission tech and the shop foreman both drove the truck listening for the sound. Found nothing unusual.
They ran some checks and tests. Checked the transmission, transfer case, front differential, front and rear drive shafts, IWEs, hoses, vacuum pressures, and made sure there was sufficient fluid in all parts.
I went to pick up the truck, and had the shop foreman himself sit with me while I drove the truck. I put it into 4A, and showed him the noise I hear. He heard it clearly, and said that's a normal sound of the 4x4 system, nothing to worry about. I believe he said it was the sound the front drive-shaft/chain assembly makes when it has power flowing through it.
Sounds like a tiny coffee percolator, or small chains rubbing on the ground. A light aluminum metal kind of sound.
Anywho! Hope this posts helps!
BTW: I did try to capture the sound on my iPhone 6S+, but was unable to hear it. It's pretty faint, but noticeable as I drive this often.