Recently I was driving a 99 Suburban 1500 4x4, with the action, sounds you described while stopped. According to the owner it was normal, at times you really couldn't feel the 4x4 engage while moving and the only indication that it was in 4 wheel mode that there wasn't any wheel spin as all the indicator bulbs were burnt out.
Drove it for 4 days like that on slimy mud and dirt and wet asphalt.
My own 4x4's are all Dodges, the 99, the only time that I stop completely, shut off the engine and go into neutral, foot on the brake is the 2wd Hi to 4wd Lo mode. 2Hi to 4 Hi is always on the fly, but not under load or spinning. It has a vacuum operated locking sleeve on the right side of the axle that locks everything in and gear cluster in the transfercase, it will not engage if you are spinning. I try to lock in before I need 4x.
On the 03 it has electronic transfercase and I haven't ever went into 4low, 4 Hi and diesel power has got me thru.