Some resources are obvious places to look. Checking the past equivalents of today's Encyclopedia of Chess Opening and Modern Chess Openings is a good start (note: MCO, from its first edition in 1911, has not had coverage).
The Handbuch des Schachspiels, for example, has a Jerome Gambit game reference in its 8th edition (1916) but nothing in its 7th (1891) or 6th (1880) editions.
Cook's Synopsis of the Chess Openings, 1st and 2nd editions (1874, 1876) have no coverage of the Jerome, while its 3rd edition (1882) does.
The first edition of Chess Openings Ancient and Modern (1889) has analysis. Steinitz' Modern Chess Instructor, Part II (1895), of course, has nothing.
There are many other 19th century chess books touching on the opening – and many, many more, not – and each must be checked for Jerome Gambit material.
Some past authors are apparently ambivalent about the line. G.H.D. Gossip's 1891 Theory of the Chess Openings has nothing on the Jerome Gambit, while his The Chess Player's Vade Mecum and Pocket Guide to the Openings, also published in 1891 does have analysis. Gossip out-does himself in his (with F.J. Lee) 1903 The Complete Chess Guide by writing one place that he has "eliminated obsolete openings" such as the Jerome Gambit, which he mentions by name, and then, later on in the book, he gives analysis of that same opening.
