Hi there. I did a bunch of search's on site for information about this and didn't find anything.
If its already here somewhere I apologize, but if it isn't, read on.

I recently purchased a used 2000 Silverado with the center jump seat, also referred to as the center console, that mostly wouldn't open. Occasionally when you pushed on the latch release it would work but most times not.

After searching around on the web I found that its a not uncommon problem with the "safety" lock out that prevents it opening unless its in the horizontal position. This mechanism is a plastic "rod" that rolls up and down an incline to block the release latch movement. Of course over time and with use the rod starts to stick and no longer rolls freely. Which is where I was at...

After a brief attempt to work on it in place I removed it and took it inside. There's one bolt on the drivers side and two bolts and a screw on the passenger side.

Then the trick is to get it open, which means getting the rod forward enough for the latch to work. If you look through the small gap below the latch you can just see the rod.
If you have a dental pick try to gently loosen it and tip the console until it moves forward and allows the latch to release.

Once the lid is open, to get to the latch assembly you need to remove the coin holder, this is held in place by four plastic latch/hooks. So the only way is to gently pry around the edge until it pops out. Mine had already been apart once and two of the receiver parts were broken.

So now its all open and hopefully you haven't broken much. ;)
So all that's left is to clean and reassemble. The plastic on my rod seems to be deteriorating with age and if it starts sticking again I'll be looking for some wood doweling to replace it.

get a high quality lock lube from a locksmith and spray the mechanism with it. A small amount of the lube goes a looooooong way. Had the same problem with mine and the lube worked wonders. Has not stuck closed since.