You've had a lot of suggestions. Unfortunately none of them work. Even a straight pin is too big. I tired paper clips of all sizes, sewing needles, pins of all kinds, and my Nexus 7 tool. And here's the distressing thing. LG doesn't have any of the OEM ones available. They make the hole so small nothing else fits and then can't supply. AT least they can tell you something. Google support for devices is limited to morons who can only tell you to send the whole thing back for replacement. They didn't even have a phone number for LG in case you need repair or parts. Google needs to rethink actually trying to handle the sale of devices on their own.
And now the good news. My wife had an earring that the back pin was small enough to work if you pushed it very hard into the hole.