Holed ,both ends.
The center shows it had studs or similar , for
Cuff-link did come to mind.
An escutcheon for a gunstock was limited only by the makers whim. Many were consistent ,but reflected different era's and "schools" of build. (School meaning region and nationality type of gunbuilding ,sometimes blended with locale's desires and influence.)
Grotesque for example were popular in a place and time.
Few were pinned or nailed but rather carefully inlaid.
Pistol butts could have a cap or similar ,and two fasteners would be fine. Too ,a stud inletted in the wood could have been employed.
None come to mind that are similar though.
With the liberty of artistic creation ,and humidity vs dryness causing wood to expand and contract ,could a gun maker secure a thumbpiece on top of a stocks wrist so securely? Sure.
Never viewed cuff-links holed like the o.p.'s sample ,but jewelers had creative liberty too. L.o.l..
An inlay for a walking stick/cane?
Some well to do lady's brush handle?
Ornate bling for something. Makes it a keeper find....