Welcome aboard!

This sounds like something we haven't visited in quite a while, but I hear about it from time to time. It can happen on any later year GM and others, and more so on longer wheel bases. Rear leaf spring wrap, combined with slip-yoke friction. It goes away with 4x4 engaged because the spring wrap is greatly reduced (the rear axle alone isn't reacting to the entire mass of the truck), as is the slip-yoke movement. The solution is inexpensive, and very easy to do. Simply grease the slip-yoke spline. I like high pressure marine grease, although GM suggests lithium grease (common chassis grease). It's also a good time to refresh the U-joints (and center carrier, if it has a 2-piece shaft), the rear transfer case shaft seal on older vehicles (the seal hardens over time, and can weep ATF), and the transfer case ATF. Drain the transfer case (Dex-VI ATF, less than 2 qts), disconnect the U-joint at the rear diff (mark the pinion yoke and rear shaft, so the U-joint can be reinstalled where you found it), and slide the slip-yoke out of the transfer case (ATF will run out if you didn't drain it). Apply grease to the entire circumference of the internal spline of the yoke. It only needs a coating that will distribute as the spline is reinserted. I use a good size dab on a fingertip, and wipe it into the spline grooves an inch or two deep. Work the spline in/out a few times as it's inserted into the transfer case to distribute the grease (apply a little ATF or grease to the outer yoke surface to lubricate the seal). Return the remainder of parts where you found them, fill the transfer case, and be done with it, at least for a long while. The transfer case service interval is about 50K miles, so if this is done at that time, you should not experience the problem again.