Great button, many 60Th Regiment buttons were found in Lower Manhattan, When they were digging for the sites of modern skyscrapers, in the mid eighties. The 60Th Regiment were stationed in many various camps and fort sites here in New York City. On page 45 of my book "New York City's Buried Past" A Guide To Excavated New York City's Revolutionary War Artifacts 1776-1783 I have a sketch of that button.
The book is out of print, and hard to find. Currently some one is selling a few copies on eBay.
PS. Don T. Purchased the 100Th copy from me when the book first came out in 1992.