Turns out we had a busted snap ring on the transfer case output shaft. Got a tip from user on a Facebook forum (F-books group Dodge Ram Trucks 2nd gens; user Don Huffman) my daughter posted on. Giving credit where due.I verified it by pulling the speedometer gear and using a pry bar gently pushed back and forth on the output shaft trying to ensure I was pushing on the snap rings that hold the output shaft speedo gear on. See pictures for excessive total movement. Easy fix with a $5 snap ring. Other more expensive and more robust solution are available. For example,
Sonnax T-Case Saver Google T-Case Saver for more.

Edit (1st pic: shaft back, 2nd pic: shaft forward, 3rd: busted old ring, 4th; new style upgraded ring installed)