I am a bit behind in reading Dennis Monokroussos' "The Chess Mind" blog, and I just discovered - in Dennis' past review of Taming Wild Chess Openings, that the Jerome Gambit actually does appear.
My mistake. I had looked in the book's "Contents" without success. I had checked out the "Index of Moves and Variation Names" without discovering either the Italian Game, the Giuoco Piano - or the Jerome Gambit. Ditto the "Opening Index".
Ah, but Dennis pointed out - the Jerome is covered in the "Evans Gambit: Lasker Defense (C52)" chapter!
4.Bxf7+? Kxf7 5.Nxe5+ is the Jerome Gambit, which, however, is refuted by 5...Nxe5 6.Qh5+ (6.d4 Qh4! 7.0-0 Nf6 8.dxc5 Qxe4) 6...Kf8, or here 6...g6 7.Qxe5 Qe7, winning.Regular readers are no doubt familiar with the "pie-in-the-face" (6...Qh4), Jerome (6...Kf8) and Whistler (7...Qe7) defenses.
My apologies to John and Eric, and my thanks to Dennis.