Same problem, back hatch would not lock, 02 Tahoe Z71 stock.
I fixed the problem by pressing the two buttons on the remote at the same time for iirc 10 or 15 seconds, im not sure but again iirc this reinitializes the remote to the reciever, anyhow it still wouldn't work. Somehow or other I ended up pressing the lock button twice while testing got the honk then pressed the lock button again, so 2 honks, amazingly after the second honk the back hatch and all the doors were locked.
Ive since tested this multiple times, one honk locks all the doors 2 honks locks all the doors as well as the hatch.
Theres nothing in the manual about this that I could find.
Keyfob is stock, stupid luck figuring this out, or im a genius, you pick lol
Edit- If I had to guess id say that reinitializing the remote wasnt necessary, just try pressing the lock button 3 times.