Looks like maybe you should get a book on the KG. You won't get many good, in-depth answers from a chess.com forum.
How to play the Falkbeer counter gambit? (King's Gambit Declined)

And honestly, if you're studying this for use as black (which appears you are) I wouldn't spend to much time on it, not many people play the King's gambit. But what do I know, I play 1. ..c5. Do you see the KG a lot?

Never mind what the book line is. Just play the best you can from here. You already achieved your objective... to derail the KG. If you aren't playing mano a mano from here out and your opponent so prepared that he already has a fatal trap in mind then dealing with one extra move isn't going to help you.

There is a line in the Falkbeer Counter Gambit in which black just pushes the e-pawn ( 3. ... e4 ) and is willing to sac it should white attack it with the d-pawn ( 4. d3 ) by pushing it even further ( 4. ... e3 ). I encountered this line in the demo version of some chess teaching program. Being two pawns down is not that great I thought to myself. But the Kings Gambit came up in a recent sudden death game of mine and I decided to give it a try. My opponent seemingly unfamiliar with the position chose to attack the pushed pawn with the knight instead. The result was shocking:
It may be that the Falkbeer Counter Gambit is objectively somewhat more favourable to white than some other defenses to the Kings Gambit but in a quick game it seems far more playable since black has a very comfortable development and not many issues that need long thinking ( not to mention the element of surprise ).

Looks like maybe you should get a book on the KG. You won't get many good, in-depth answers from a chess.com forum.
Seconded, except for the typo in "[m]any".

Interestingly the Falkbeer transposes to the Scandinavian Defense in some lines. So you might also like to look at the Scandinavian. It is always helpful not to just look at opening lines in books but to go through entire games from databases which show you how the masters handled the resulting middle and end games.
Okay so basically the Falkbeer counter gambit goes 1. e4 e5 2. f4 d5 3. exd5 e4
2. The c4 pawn.