That is a very cool find! it certainly looks like it could be a pistol butt-cap! Here is picture of a British model 1780 cavalry pistol pictured in
The Revolutionary Soldier 1775-1783 By C. Keith Wilbur.
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The piece you found and the butt-cap on the pistol in the picture look quite similar. The Royal Navy button and musket balls also make me think this is likely from a pistol. In your case, if the item you found is from a pistol, it may be from a sea service pistol. The difference from a cavalry pistol, is the sea service pistol has a belt clip on the back of the pistol:
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Only reason why this may not be a pistol part is because most British pistol butt-plates were made from brass.