Just for info, there were no contingents of the 46th assigned for duty in the War of 1812. The regiment had arrived back in Britain in December 1811 after service in the West Indies, temporarily leaving behind a flank contingent of four companies who arrived back in Britain in June 1812 at the outbreak of the war. The regiment was then re-consolidated on the island of Jersey in the English Channel and embarked in toto for Sandown Barracks on the Isle of Wight, where it remained until August 1813. There, they received orders to proceed to New South Wales in Australia, arriving in February 1814, and were stationed there until September 1817 when they re-embarked for service in India.
However, the button doesn’t match to any of the documented British patterns for the 46th in either that period or the Revolutionary War period as far as I’m aware, but that doesn’t necessarily rule out it being British. Apart from the possibility of buttons mismatching to geographic deployment of regiments, one other thing worth pointing out is that British regiments on long tours of duty abroad would sometimes fulfil any need for replacement buttons (and other items) using ‘local’ producers and non-standard patterns. However, my gut feel is that it isn't British. Other than that, I can’t help much.
