The Gospel is not a call to action. It is not an exhortation. Instead, the Gospel means "good news." It is the proclamation of a historical event that included the incarnation of the Most High God as the Son of God Jesus Christ, His substitutionary life and death for sinners on whom He chose to have mercy, and His resurrection from the dead. The Gospel declares God's justice in punishing sin, manifests the only way to appease (or propitiate) God's wrath against sin through the crucifixion of Jesus, and shows His mercy in justifying ungodly people who believe this good news of salvation by graciously forgiving their sins, imputing to them righteousness, giving them peace with God, and bestowing on them eternal life.
Believing the Gospel is not performance of an action. This means that believing the Gospel cannot mean turning from sin, surrendering your life to Jesus, committing your life to Jesus, asking Jesus to come into your heart, having a relationship with Jesus, or performing some mystical and elusive act of resting or trusting. The object of belief can never logically be a command to do something. For example, it doesn't make sense to say, "I believe 'Repent and believe the Gospel!'" The command to "Repent and believe" points us to the Gospel, but it isn't the Gospel, and regrettably, many people use this command to conflate repentance and belief instead of keeping them separate. In contrast, the object of belief must always be a proposition (i.e., a declarative statement or assertion). The content of the Gospel is a proposition, so it can be the object of belief, as in the sentence "I believe the Gospel." Believing a proposition means to be convinced that the content of the proposition is true. This means that believing the Gospel means being convinced that the content of the Gospel is true, even as Abraham and Sarah were convinced that the proposition given to them by God in the form of a promise was true (Rom. 4:21-22, Heb. 11:11). By this we can understand that believing the Gospel is not an action, but the persuasion of the mind that what God did through Jesus is true.
The Apostles confirm this. For example, John described belief as follows, "If we receive the witness of men, the witness of God is greater; for the witness of God is this, that He has borne witness concerning His Son. The one who believes in the Son of God has the witness in himself; the one who does not believe God has made Him a liar, because he has not believed in the witness that God has borne concerning His Son" (1 John 5:9-10, and see also 1 Thess. 2:13, as well as 2 Thess. 1:7-10 and 2:10-14 where obeying the Gospel is basically equated with believing the apostles testimony). Receiving the witness of God is exactly the same as receiving the witness of men, except for the fact that the witness of God is more authoritative and receiving it results in eternal life (1 John 5:11-13). Everyone who believes God's witness about His Son has the witness in himself, meaning that he received the witness as being true (i.e., he was persuaded of it). People who don't receive the witness as being true have made God a liar. Likewise, "What He has seen and heard, of that He bears witness; and no man receives His witness. He who has received His witness has set his seal to this, that God is true" (John 3:32-33), and then immediately after this, "He who believes in the Son has eternal life" (John 3:36a). In the Gospel of John, to believe in Jesus for eternal life means to be convinced that the testimony about Jesus is true, namely, that He is the Christ, the Son of God who is the Savior of the world (John 20:29-31, John 4:42, 1 John 4:14). In confirmation of this, the only passage in the Bible that defines "belief" (most often translated as "faith") says, "Now faith is the assurance of things hoped for, the conviction of things not seen", and then immediately follows this definition with an example where faith results in knowing the truth of the proposition that God created the world from nothing (Heb. 11:1-3). Applying this definition to the Gospel, none of us saw the crucifixion and resurrection of Jesus Christ, but when we believe that the eyewitness accounts given by the Apostles in the New Testament are true, we literally fulfill Jesus' words "Blessed are they who did not see, and yet believed" and are assured (and convinced) that we have "life in His name" (John 20:28-31, 1 John 5:13).
Belief in the objective truth of the Gospel brings with it joy and assurance. Many people can explain the Gospel, but because they don't have a correct understanding of saving belief, they never actually believe the Gospel. Many people think that they can appropriate the benefits of the Gospel by mixing belief with other things, such as trusting in Jesus and establishing a relationship with Him. In other words, they think that trusting in Jesus and establishing a relationship with Jesus are elements of saving belief. But they are not. Rather, they nullify belief and introduce a subtle form of self righteousness and mysticism. And it is because people are practicing self righteousness and mysticism that they have no real assurance and whatever degree of assurance they think they have is just a delusion. The fact is that no one can appropriate the benefits of the Gospel. We can't bribe God through our efforts to trust, rest, or surrender. Rather, God confers His gifts and benefits on sinners according to His own mercy and grace, and by believing the Gospel we are simply coming into a conscious understanding of what God has accomplished for us (2 Cor. 4:3-6, Col. 1:5-6, Isaiah 43:10-12). Believe the Gospel and let the truth of the Gospel be your joy and sufficiency that overflows in much praise and thankfulness to God.