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The origin is unknown, but generally credited as Irish. The "Swallowtail" title (in conjunction with the alternate title in O’Neill’s, “The Dancing Master”) may possibly refer to the type of coat with tails typically worn by early 19th century dancing masters. “Swallowtail Jig” is likely dated to the mid-nineteenth century (perhaps on the strength of its appearance in Ryan's Mammoth and Kerr’s Merry Melodies collections, published in the 1880's), and it is often used as the vehicle for Northumbrian sword dancing (for five dancers with two handled swords).
Here's a link to Tim Keough's ukulelesecrets.org where you'll find several tablature songs and instructional videos on how to play them, including Swallowtail. I've posted the tablature for Swallowtail above.