Keep in mind, that is not a lock on the tailgate. It's a key-switch to roll the window up and down (unless you have the manual rear window. I think you can have power side windows with a manual rear window). Internally there is a latch that doesn't let you open the tailgate until the window is rolled all the way down and that is the tailgate lock. If your key turns the cylinder, then you likely have an electrical problem. Does the window roll up and down with the switch on the dash? The little switch in front of the lock cylinder #9 often goes bad.
https://ck5.com/forums/threads/k5-tailgate-key-switch.339726/#post-4068922
What I remember is taking 2 nuts off to remove #11, then you can take #13 off to get #9 out.
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