Well, my Suburban's rear door lock is now working like new.
Here is a run-down of the solution (I feel like a fool - sorry to bore you with my long story):
I first bought a new lock (with its own key) for the rear door (part number given by members here). The lock matches the side door locks, the ignition lock, and the glovebox lock.
When I removed the rear door lock, I quickly realized that it was a completely different style/shape lock from all the other locks.
Before I removed the lock, I sprayed WD-40 into it. The key to the other locks goes into the rear door lock, but that key does not turn the lock. So I figured that I needed to find a new lock.
Nobody has a part number or replacement for the lock.
After talking with all the places on the Outer Banks that have lock/key department, I was unsuccessful in finding one who could make a key for the original lock. The knowledgeable key-makers told me that I needed to take the lock assembly to a real locksmith.
Yesterday, I found a locksmith in Chesapeake, VA (about 60 miles away). He said (over the phone) that he could try to make a key. I could send the lock to him or drive it to him. I decided I might as well make the 120 mile round trip (I am retired).
I went to the counter at the locksmith shop and showed the lock to the young man behind the counter.
I explained that I needed a key made for the lock (to match my other keys, if possible).
The locksmith took my lock and my ignition key (that works in the 4 other different-design locks on my Suburban).
He put the ignition key into the rear door lock, and immediately and quite easily he turned the key.
He politely said, "I do not see any problem".
I was astounded and jokingly said "you must have the golden touch".
He said, "I bet you sprayed the WD-40 into the lock while it was mounted in the rear door"?
I said yes.
He then said "the WD-40 probably could not reach the 68 year old original grease/lubricant at the rear of that small cylinder when the lock was laterally in place. During your trip here, the WD-40 got a chance to "move around".
He then sprayed his "professional" lubricant (no silicone in it) into the lock barrel, and he cleaned up the lock, and he handed it back to me.
I was astounded and I was dumfounded.
I thanked him and I asked what I owed him.
He said,"nothing".
I said "at least can I buy a small can of your lubricant spray".
He could not find a small can of the spray, so I bought the larger can of spray ($16) and handed him $20 and said "keep the change".
Ain't life grand - ain't good luck grand?