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Climb into the bed and with your trusty torx set, remove all the bolts on the inside of the tailgate, from the locking mechanism cover. Its a large panel that goes almost the full width of the tailgate.
Then you can see the vast majority of the mechanism, and repair or replace as necessary.
In a pinch, you can yank the two metal rods towards the center of the tailgate, to release it, so you can flip the gate down and work on it in a more comfortable position.
More than likely, the plastic tabs inside the handle release mechanism broke. its not all that uncommon.
Thanks frederic, was thinking that was probably the solution, but I have one of those bed liners and you can't take the tailgate section off with it closed, so I guess I will have to cut it off or something.