Maybe some unit disk?
Although it seems quite small…
34a cp., btg. Susa, 3° rgt. Alpini
Probably a compass. Seen a few of those.
This is a flintlock made without a patch box. In some areas a hole was drilled in the buttstock to hold the users favorite patch lubricant.
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Correction, post 5 should read precussion rather than flint
WJW is correct the hole held Tallow to grease patches