Calvin Espinoza, a member of a watchmakers’ group I belong to,
posted something that might be helpful. I do not know how alum might
affect pearls, but here is the germain part of his post:
There are actually quite a few ways to remove rust from a movement,
and each of its individual parts.
The way that I learned at school was to COMPLETELY strip the movement
of anything that was steel, and use alum, which “eats” steel like
acid. Since rust is just oxidized steel, it cleans right up!
Now, this ONLY works IF the part that needs to be cleaned is in
fact, NOT steel itself. Since the pillar plate/main plate is
generally made from brass and then nickle plated, you are safe.
(sidenote; this is also an excellent way to remove a broken
Del Pearson of Designs of Eagle Creek in Beautiful South Texas