Anne Geddes Gilchrist in JFSS V, #19, p. 156, 1915, gave only 2 1/2 verses, plus chorus, of "The Gentleman Solder" collected from Mr. Coomber in Sussex in 1907, and pointed out the song was on a broadside (Malcolm Douglas has above given click-ons to several copies on the Bodley Ballads website). She pointed out what appears to be the earliest copy of the tune as a untitled jig in an Irish dance music collection, and gave that tune. Here is an ABC of it from a reprint (1965) of the collection.

X:1
T:Jig, #12, R. M. Levey, 'The First Collection of the Dance Music of Ireland' (1858)
N:Also know as "Drumdelgie" and "Dydd LLun y Boreu" Q:1/4=120
L:1/8
M:6/8
K:D
F/G/|ABA AFA|d2ef2d|ABA AGF|(G3G2)F/G/|\
A3/2B/A AFA|d2ef2d|ecA ABc|(d3d2)::\
d/e/|f2fe2g|f2d {e/}dcd|ecA {B/}AGF|(G3G2)(F/G/)|\
A3/2B/A AFA|d2ef2d|ecB ABc|(d3d2)|]