Isn't anybody paying attention to the US quarter-dollar coin showing the brass hook-shaped object is at least 3.5-inches long? That's much longer than a musket/rifle sling adjuster-hook.
This 3.5"-long hook, with two rivets for attachment, could be from a US M-1851 swordbelt. (See the photo below.) But since the digger says it was found at an Indian Wars Era military site, if is more likely to be from a Model-1876 swordbelt. That being said... the shape of the curved hook on his find looks like what we see in the M-1851 photo.