IanC, referring to Holloway and Black, says:

"
It was poisoning from the mercury salts used to treat syphilis that killed him. See "The Buck's Elegy", c 1800?, in Holloway and Black's 'Later English Broadside Ballads', I, #17.
"

This doesn't quite work -- the dying buck/rake says:

Had I but known what his disorder was,
        Had I but known it, and took it in time,
I'd took pila cotia, all sorts of white mercury,
        But now I'm cut off in the heighth of my prime.

... i.e. if he'd known that the girl was poxed, he +would+ have taken mercury (then the conventional cure for syphilis). Elsewhere, there's some discussion as to which specific variety of mercury this would be. The rationale was that mercury raised the temperature and killed off the spirochetes, which was also why he was wrapped up in flannel, again to raise the body temperature.

Some glossings have him dying of mercury poisoning, but I think it's more natural to see him as dying of syphilis directly rather than from the indirect attempt to cure that disease.

The tune seems to be recorded earlier than the words, and I think there may be a split here.

Masato on "The Bard of Armagh":

"
BARD OF ARMAGH. AKA and see "Phelim Brady." Irish, Air (3/8 time, "plaintive"). D Major. Standard. One part. The air is the same as that of "The unfortuate rake," an 18th century lament which tells of a dying young man. Other songs set to the tune are, in Ireland, "The convict of Clonmel," and in America, "The Streets of Laredo, "The Cowboy's Lament" and "St. James Hospital." English derivations of the song can be be found printed in broadsides from the mid-19th century, including "The unfortunate lad" and "The bad girl's lament."
***
Oh, list to the lay of a poor Irish harper,
And scorn not the strains of his withered old hand,
Remember his fingers, they once could move sharper,
To raise up the mem'ry of his dear native land.
***
"

Splitting the tune from the words, the words strike me as distinctly late whatever-the-Irish-equivalent-for-mockney is.

Malcolm said:

"
Steeleye Span recorded an arrangement of Mary Doran's When I Was on Horseback; their text is not an independent example of that variant.
"

Thanks for this. It still leaves the problem of why Cork city on the 14th of May? but pushes it back. (The Steeleye Span version is first recorded on "Ten Men's Mop", I think).

Do you have a source for the Mary Doran version?

Thanks everybody -- despite having some long-cherished assumptions destroyed, the information deployed on this thread is marvellous.

Off to try to digest Masato's post.

Robin