Your sensor is probably shot. Does the open door light turn on the gauge cluster when you open the tailgate? Open your driver's door, look at the gauge and you should see the light come on for reference. I have never looked to see where the sensor is on the tailgate so you'll have to look around. On the doors you'll see a little oval shaped black piece of rubber and when you push it in you will see the front overhead light go off and back on when you release.
Yeah, mine does the same thing. I'm pretty sure you have to replace the entire latch. There is a small harness going to the latch, so I assume the sensor is in there. I haven't bothered to do it because it's $100!
If you can get the latch out, though...it might be worth trying to just clean up the contacts. I assume everything back there gets pretty dirty.