I am just guessing about the 18th regiment of foot but here is my logic:
1. County Wexford is Irish.
2. The Irish never invaded or otherwise had reason to have troops here except as attached to British militia.
3. A google search of County Wexford militia yielded a reference to incorporation into the 18th regiment of foot.
4. The 18th regiment of foot was comprised of various Irish militia including a company from County Wexford.
5. The history of the 18th regiment of foot shows they were all over the colonies during our revolution.
I could be totally wrong but that was my quick history according to google.
The most detailed description about the association between the Wexford County Militia and the 18th is in this book excerpt link:
The button is absolutely incredible. I imagine that is is a very rare example of a precious piece of Revolutionary War history.