Hmmm... I looked at it a little more carefully, and I have a bad feeling I brought this on myself. I had the plastics off over the weekend to replace the rear brake cable, and I think I messed something up on the reinstall.
When I push the key in to open the box, the latch releases and the door opens an inch or two. Then it gets stuck and I need to jiggle the door to have it open up from there.
Once it's open, I feel like the glove box door is very loose, which I don't recall before. It seems to me that the lower hinges are probably supposed to click into something inside the glove box / behind the kick plate. And I probably knocked it out without noticing until now
Referring to the parts diagram (copied below), the blue "hinges" are the parts I think are loose. I can actually remove that glove box cover with the kick plate installed, so there is nothing holding the hinges in place (which I think is the problem).
It seems to me those hinges either need to snap into something behind the kick plate, or this mysterious part called "square" (circled red) is supposed to hold things in place and has come loose.
Can anyone shed any light?
The unfortunate thing is that I find it such a pain to take off all the plastics that I'll probably live with this problem until the next time I am compelled to open the bike up for other reasons. At least I'll wait until the clock battery dies!