I took one off a long time ago but can't recall exactly how it was held on. I seem to recall some sort of retainer ring around the back end of the lock. Once you release that it should pull forward through the hole.
Found this on another site so it looks like you need to insert the key to remove the lock...
Here is the procedure to remove the lock cylinder from the glovebox from the Ford 86 shop manual.
1 Insert key into lock cylinder.
2 Insert a wire or bent paper clip into the small hole in the latch. Push the wire on clip to depress the lock tab & release the lock cylinder & key.
3 Remove the lock cylinder.
note: if the glove compartment key is not available, press each lock tumbler lightly while gradually pulling lock cylinder out. Do not press tumblers too far, or cylinder cannot be removed.
Hope this helps you out.
If you don't have the key or can't do as described above without a key then you can also replace the whole door from a junkyard if you can find one of that year with the keys inside...
That creates an extra key situation but you can also change the door locks fairly quickly if you can find a set with the keys. Door locks are actually easy as they are held in buy a horseshoe clip...just be gentle with the connecting rod as the clip is made of plastic that is probably older than most TRS members...lol
More work but I've done it a few times for just such a reason...lost the key.
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