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I have been able to get a flat screwdriver into the gap between the gate and bed cornor to persuade the latches free to open the gate.
This is a temp fix as, most likely the latch is worn, bent or both. There are kits out there to replace the internals but I have never used one. I usually only have trouble when I a big load of wood on and it spreads the bed or pushes on the gate.
The kits are easy to installl. Leave the tail gate on the vehicle. Remove the handle bolts and the screws on the ends. Disconnect the cables on the handle and pull out (By the way attach a fish tape to the cables on the handle side). This will make the reinstall much faster. A good shot of WD-40 or Penetrating oil would help once you get the tailgate open on the ends and the handle. A shot on the latch and the two ends keep it well lubricated. I do this with every oil change.
I've never tried it with the tailgate up, and it may depend on what, if any, bedliner-type cover is on the tailgate, but can you remove the access panel from the inside of the tailgate? This may gain you access to some of the latch components so you could spring it open...