Found this item today. Non- ferrous metal with two countersunk holes. Measures 2" x 4-1/4". No markings and no known military activity in area. I was thinking butt plate but don't really know. Let me know if any other details are needed. Any help with ID is greatly appreciated!
Your recoil plate is from a British Land Pattern musket ('Brown Bess') or one if its derivatives - regardless of which pattern, your plate dates 1720s-1830s.
Given your location, I think its safe to assume yours is from the American Revolution.
Here is your plate pictured on the stock of a surplus India Pattern musket that was also used in a Revolution - except it was the one fought here in Texas. The musket pictured below was already outdated when it was being carried by a mexican 'cazador' from the San Luis Potosí battalion in 1836.