"Old buffer" in a general sense goes back to the 18th century.

In the 1873 version, the earliest discovered, the "old buffer" is a soldier who calls for "six stalwart lancers" to carry him.

The fabulous Traditional Ballad Index refers to a text from 1826, but that's a longer and more elaborate song, related to both "Tarpaulin Jacket" and "Rosin the Bow." (And published when Whyte-Melville was only four or five years old!)