The Laborer on Election Day performed by Katherine Rhoda
Though pre-19th Amendment and thus about male voters only, The Laborer on Election Day, from the 1874 songbook The Trumpet of Reform: A Collection of Songs, Hymns, Chants and Set Pieces for the Grange, the Club, and All Industrial & Reform Organizations, is worth a look. Words are by J.G. Whittier, who I assume to be Quaker poet and abolitionist John Greenleaf Whittier, and music by G.F. Root, presumably George F. Root who edited the collection and who wrote a number of noted Civil War songs. The whole songbook can be downloaded for free at https://archive.org/details/reformc00root This song is #76, on p. 81 of the PDF.
Read more from Katherine about historical songs about voting here.