Try these (copy & paste). The first one will be a bit less than one page but very specific. The second one is two pages with some riffraff thrown in.
+glove +latch +broken
+latch +broken
You are about to discover that the latch itself is broken and in all probability can't be fixed. I tried to fix mine earlier this year but found the latch mechanism is molded with fragile elements that couldn't be glued/epoxied/JB welded because the parts were too fine and the clearances too small. My latch spring was also broken but I was able to find a work-around for that. The only solution is to replace the entire glove box, expect to pay ~$100 if you opt for a new and known good box.
You may get lucky though. You can take an aerosol spray like WD-40 or preferably a silicon or Teflon spray and hose the latch area and see if it frees up. Be aware that on your Gen I the fuse blocks are in the area and over spray could get on them.
Take a look at the tab on the lid, the tab should have an unbroken rectangular hole. Take a look in the hole the tab of the lid fits into next to the button, you should see a horizontal post with a chisel shaped tip protruding into the opening. When the key is off the post should not move. With the bike in neutral and the key on you should be able to move the post by pressing on it horizontally toward the gas tank.
Just to be sure that it is the box, put your ear on the box or the faring next to the box, be sure your FJR is in neutral, then turn on the key. You should be able to hear the solenoid go CLICK. This means the solenoid is good.
For right now I have RTVed a magnetic cabinet closure to the box and the magnetic plate to the lid and it works just fine.