I used to call this the Kentucky Opening. For a while after its introduction it was greatly favored by certain players, but they soon grew tired of it.The issue of the "Kentucky Opening" has been dealt with previously on this blog - see "The Kentucky Opening" parts 1, 2, 3, 4 and "The Kentucky / Danvers Opening".
That the Jerome Gambit had been "greatly favored by certain players" seems to suggest that games should be available - but none new to me have surfaced so far.
Blackburne may have been referring to coverage of the Jerome Gambit in some print sources.
For example, The Chess Player's Chronicle, August 1, 1877, translated and reprinted the early and in depth article on the Jerome Gambit, from "Chess Theory for Beginners" by Lieut. Sorensen, from the May 1877 issue of Nordisk Skaktidende. I believe that the translation was by Rev. C.E. Ranken.
Later, the third edition of Cook's Synopsis of Chess Openings A Tabuled Analysis by William Cook (1882) had Jerome Gambit analysis, including thanks to
Mr. Freeborough of Hull, and Rev. C.E. Ranken, of Malven, for material assistance in the compilation of the tables, original variations in the openings, and help in the examination of proof.Versions of Chess Openings Ancient and Modern, starting with the first edition in 1889, include Jerome Gambit analysis and suggested moves by Freeborough and Rankin.
It should be noted, too, that George Hatfield Dingley Gossip covered the Jerome Gambit in his Theory of the Chess Openings (1879) and The Chess Player's Vade Mecum (1891). James Mortimer also had Jerome Gambit analysis in the many editions of his The Chess Player's Pocket-Book, starting in 1888.
Freeborough and Ranken, Gossip and Mortimer - merely commentators or players?