One way to get a feel for a particular opening variation is to play over a selection of games by someone who is exerienced and knowledgeable in that line.
The FICS player Petasluk has 562 games in The Database, starting in 2004. His play against the Jerome Gambit declined is educational.
Petasluk - bozidaranas
5 0 blitz, FICS, 2023
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
4...Kf8
The Jerome Gambit declined.
If it were capable of feelings, Stockfish 15 would be puzzled by this move, as it assesses the capture of the Bishop as about 3 3/4 pawns better for Black, while it sees this refusal to capture as about 2 1/4 pawns better for White.
On the other hand, the psychological intent is clear: Black decides that if White wants him to take the piece, then he will decline it.
5.Bxg8
Simply taking care of business.
He could retreat the Bishop to d5 or c4 or b3, or he could go for complications with 5.Ne5. He decides that being a pawn ahead, with Black's King disturbed, is enough.
All of this takes place in the context of this being a 5-minute blitz game.
5...Rxg8
Already a small slip, as 5...Kxg8 is a bit stronger. Indeed, Petasluk has faced that line in a few games
6.O-O d6 7.c3 Qf6 (7...Bg4 8.d3 h6 9.Be3 (9.h3 Bh5 10.g4 Bg6 11.Be3 Bb6 12.Nbd2 Kh7 13.Nc4 Rf8 14.Nxb6 axb6 15.Nh2 d5 16.Qc2 dxe4 17.dxe4 Kh8 18.Rad1 Qe7 19.Rd5 Rad8 20.Rfd1 Rxd5 21.Rxd5 Rd8 22.Qd3 Rxd5 23.Qxd5 Qh4 24.Kg2 Qe7 25.Nf3 Qd6 26.Nh4 Qxd5 27.Nxg6+ Kh7 28.exd5 Black resigned, Petasluk - bijeli, 5 0 blitz, FICS, 2014) 9...Qd7 10.Nbd2 Kh7 11.Nb3 Bb6 12.Bxb6 axb6 13.d4 exd4 14.cxd4 Rhf8 15.d5 Ne5 16.Nbd2 Nxf3+ 17.Nxf3 Bxf3 18.gxf3 Qh3 19.Kh1 Rxf3 20.Rg1 Rxf2 21.Rxg7+ Kxg7 22.Qg1+ Kh7 23.Qxf2 Rg8 24.Rg1 Rxg1+ 25.Kxg1 Qg4+ 26.Qg2 Qxe4 27.Qxe4+ Black resigned, Petasluk - icexman, 3 2 blitz, FICS, 2022) 8.h3 Be6 9.d4 exd4 10.cxd4 Nxd4 11.Nxd4 Bxd4 12.Qc2 c6 13.Nc3 Rf8 14.Be3 Bc4 15.Bxd4 Qxd4 16.Rad1 Qe5 17.Rfe1 h6 18.b3 Be6 19.Re3 Kh7 20.Rg3 Rf4 21.Re1 Rhf8 22.Rf1 R8f6 23.Re3 Black forfeited on time, Petasluk - sailingsoul, 5 0 blitz, FICS, 2021.
There is also the idea from mainline Jerome Gambit theory, 6.Nxe5 Nxe5 7.d4, which is also better for White.
6.c3
Preparing to build a pawn center. He has also played
6.O-O d6 7.c3 Bg4 8.d3 Qf6 9.Be3 Bb6 10.Nbd2 h5 11.Bg5 Qg6 12.h3 Be6 13.Kh2 Ke8 14.Be3 Kd7 15.Bxb6 axb6 16.b3 Raf8 17.d4 Rh8 18.dxe5 Kc8 19.exd6 cxd6 20.Qe2 Qf6 21.Rac1 Qf4+ 22.Kh1 g5 23.Qe3 g4 24.Qxf4 Rxf4 25.Nd4 Bd7 26.g3 Rf7 27.h4 Rhf8 28Kg1 Kb8 29.Nc4 Rf6 30.Rcd1 Ne5 31.Nf5 Bb5 32.Nfxd6 Nf3+ 33.Kg2 Bc6 34.Rd3 b5 35.Na5 Kc7 36.Nxc6 Rxd6 37.Rxd6 Kxd6 38.Nd4 Ne5 39.Nxb5+ Kc5 40.Nd4 Nc6 41.Nxc6 bxc6 42.Re1 Kd6 43.Re3 Ke5 44.f3 gxf3+ 45.Rxf3 Rxf3 46.Kxf3 Ke6 47.Kf4 Kf6 48.e5+ Ke6 49.Ke4 c5 50.c4 Ke7 51.Kf5 Ke8 52.Kf6 Kd7 53.e6+ Ke8 54.Ke5 Kf8 55.Kd5 Ke8 56.Kxc5 Ke7 57.Kd5 Ke8 58.c5 Kf8 59.c6 Ke8 60.c7 Kf8 61.Kd6 Kg7 62.c8=Q Kg6 63.Qg8+ Black forfeited on time, Petasluk - Notowar, 5 0 blitz, FICS, 2011; and
6.d3 h6 7.Nc3 d6 8.h3 Nd4 9.Nxd4 Bxd4 10.Ne2 Kf7 11.Nxd4 exd4 12.Qh5+ Kf8 13.O-O Qf6 14.f4 Ke7 15.Qd5 Be6 16.Qxb7 Rac8 17.Qxa7 Bd7 18.e5 Qg6 19.Qxd4 Bxh3 20.exd6+ cxd6 21.Qe4+ Qxe4 22.dxe4 Bd7 23.c3 Bb5 24.Re1 g5 25.f5 Kf6 26.Be3 Rge8 27.Bd4+ Kf7 28.Rad1 Bc6 29.e5 dxe5 30.Bxe5 Ra8 31.Ra1 Ra5 32.Bd4 Rxf5 33.a4 Rb8 34.b4 Bd5 35.a5 Kg6 36.a6 Ra8 37.a7 Rf7 38.Ra6+ Kh5 39.Re5 Bb7 40.Raa5 Rf4 41.Rf5 Rg4 42.Rf2 Re4 43.Raf5 Kh4 44.Kh2 g4 45.g3 checkmate, Petasluk - bozidaranas, 7 0 blitz, FICS, 2021.
6...d6
Petasluk has also seen the more aggressive 6...d5 7.d4 dxe4 8.Ng5 exd4 9.Nxe4 Bb6 10.Qf3+ Ke8 11.O-O Rf8 12.Qh5+ g6 13.Qxh7 Bf5 14.Ng5 d3 15.Re1+ Ne7 16.Ne6 Bxf2+ 17.Kxf2 Rf7 18.Qh8+ Kd7 19.Qxd8+ Rxd8 20.Nc5+ Kc8 21.Bd2 Nd5 22.Na3 a6 23.Kg1 Rdf8 24.Rf1 Bg4 25.Rxf7 Rxf7 26.Rf1 Re7 27.Re1 Re2 28.Rxe2 Bxe2 29.Kf2 Kb8 30.Nc4 Ka7 31.Ne5 b6 32.Ncxd3 Bxd3 33.Nxd3 Black resigned, Petasluk - frizerkaHR, 5 0 blitz, FICS, 2017.
7.h3 Qf6
Black wants to prevent d2-d4.
8.O-O Be6 9.d4
Anyway.
9...exd4
I am reminded of the song from "The Sound of Music", "How Do You Solve a Problem like Maria?"How does White solve this position? Hint: despite Black's advantage in development, Stockfish 15 assesses White as being about 2 1/2 pawns better.
10.Bg5
Attack the Queen - development with tempo.
There was also the quirky 10.cxd4 Nxd4 11.Ng5 threatening to fork King and Queen 11...Ke8 12.Nc3 asking for the return of the tempo, which Black obliges 12...h6 13.Nxe6 Nxe6 14.Be3 Rf8 and after 15.Bxc5 dxc5 16.Qb3 b6 17.Nd5 Qf7 18.Rad1 c6 19.Qa4 Qb7 20.Ne3 Nd4 21.Nf5 Nxf5 22.exf5 Rf6 23.Rd3 Kf8 24.Rfd1 Qe7 25.Rd7 Qe2 Stockfish 15 rates White being up 2 1/4 pawns. Looking the resulting position over, I don't really understand the computer. I'm with Petasluk here.
10...Qg6 11.cxd4 Nxd4 12.Nxd4 Bxd4 13.Qxd4 Qxg5
What is going on? Who is better? What does White need to do?
A reasonable place to start would be to ask the safety question, What does Black threaten?
14.Nc3
Okay, a quick look - which is sometimes all that you have in a blitz game - would show that White can add to his development, support his e-pawn and link his Rooks with this move. But - he risks turning the advantage over to Black.
14...a6
Fair enough. White misses something, and Black misses it back.
Without a ticking clock it is possible to catch 14...Bxh3 15.g3 Bxf1 16.Rxf1. This suggests that White's last move should have been the disruptive 14.f4, although the somewhat clumsy 14.Qc3 would also have worked.
15.f4
No harm, no foul.
15...Qf6
Now a Queen exchange would calm things, but Black's move allows a pawn advance which is decisive.
16.e5 Qf5 17.g4 Qc2 18.Rf2
Awkward.
18...Qd3 19.Qxd3 Black resigned