There are a number of tunes called 'The Peacock' or variations thereon. One, current under that name in the later 18th century throughout Britain and Ireland, begins in much the same fashion as 'Whip Jamboree'. It was later used for the Scottish song 'Goodnight and Joy Be Wi Ye A', which in turn (though much later) became popular in Ireland as 'The Parting Glass'.

Whether it's the fife-and-drum tune you heard I wouldn't know, but you might have a look at the Early American Secular Music and Its European Sources website, which lists one or more 'Peacock' tunes (the incipits differ, so more than one may be involved) with references to two sets of late 18th century drum notation.

Text Index: PEA