Quoting from Clasps: 4000 Years of Fasteners in Jewellery, by Anna Tabakhova [who is a member of Pearl-Guide, username CLICLASP], p. 259:
DOUBLE SLIDING BALL CLASP
Designations:
Double sliding ball clasp, two sided ball and slide clasp or double ball slide clasp.
Description:
One end of the necklace ends with a ball (or any other shape), which slides into the groove of a decorated fitted box until the stop where the necklace is suspended. When the clasp is equipped with this device on both ends it thus becomes removable.
Dating:
Mid-20th century, American patented 14K gold clasp.
(cf. Linda Ladurner, page 150— cf. Clair Wolfstirn, page 196).
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This tells us nothing about your pearls other than dating when they were likely strung, but that is one cool clasp!
Edit:
The OP and I PMed about her pearls. They are a mid-century 3.5 momme strand.