Yes, it's supposed to open. The handle in the middle opens the whole back hatch, the handle on the right opens just the glass. You may have to close it a little hard. I swear sometimes I think my kids are going to break it they slam it so hard. If it pops open from being closed, that's another thing.
Get a Bentley's manual (link at top "Bimmer Books"), lots of good stuff in there.
Geez, 76k miles on a '92? It's hardly broken in yet!