After literally dozens if not hundreds of attempts to get this thing to proc for my monk, I noticed it could be Traded, so I got an enchanter to try it out. He equipped it and cast Identify (on himself, holding nothing) and it procced several times in a mere 10 casts, giving an emote that described (in riddling fashion) how to open it.
The enchanter also tried the Identify AA, and it also procced more than once in 10 tries, though it seemed less often than the spell.
I took the item back and again tried both the AA and a clicky (Holgresh Grand Vizier Beads) several more times, but neither would proc for me. My guess is that the item mostly procs for the spell, and that casters have some sort of bonus, analogous to Weapon Affinity for melee, that adds to their proc rate on the cast and even adds to the base 0% proc rate for the AA. Oddly, the enchanter could never get the clicky to proc, either.
Anyway, if you're a melee wondering how anyone ever figured out what to do with this locket, the secret is to get a caster to help!