For future reference, if epoxy doesn't hold that pearl, here's an old-timey pearl peg mounting solution. Cut a slit in the top of the peg - obviously use a very narrow blade! Make a tiny wedge to go in the slit. Place the pearl over this wedge stuck in the slit and force the pearl down. This pushes the wedge down into the slit; it spreads the slit apart and against the side of the hole. It goes without saying that the length of the peg plus wedge must fit within the depth of the hole in the pearl.
Do make your client aware that this is NOT going to come off. Removing the pearl means destroying it, and replacing the peg on the mounting.
Just another way to 'skin the cat' as they say. I really prefer the long-curing epoxy and a roughed up peg, but there are some clients who manage to loosen epoxy!
Judy in Kansas, who is woefully neglectful in cleaning up the garden detritus. On the other hand, it's not going anywhere!