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Note that the old version of Andrew Kuntz's 'Fiddler's Companion' at Ceolas is obsolete. They refused to allow him access in order to update it, so eventually he moved it to  http://www.ibiblio.org/fiddlers/

The old version remains online, but only because the people who run Ceolas are too lazy to remove it. It should not be used as a reference; especially without providing a proper link or attribution when copy-and-pasting it.

As it happens, the entry in the new iteration is as yet unchanged; it would benefit from the inclusion of some of the information already given here. I'd add a few references to earlier discussions:

Add: Poor Old Man (Thread 'Songs of the Sailor and Lumberman'; with tune)
ADD: Jaw Bone (Pope's Arkansas Mountaineers) (Thread 'Jawbone Origin and Categorization')

'Richie' should remember at least the second of those discussions; he started it.

Presumably there is a connection between the Minstrel song and the 'Old Horse' shanty, to which there are also references in the Forum and DT. The latter, in turn, has some connection with the 'Old Horse' of British tradition; though that song belonged to a luck-visiting custom. Further references to that, too, can be found via the search engine. 'Q' would be the man to take discussion of the American aspects further, I should think.