No. “Gospel” in the Gospels is a reference to the good news promised by the prophets of the Old Testament, and there is no mention of water baptism in the Old Testament.
(Mar 1:14-15 ESV) Now after John was arrested, Jesus came into Galilee, proclaiming the gospel of God, 15 and saying, “The time is fulfilled, and the kingdom of God is at hand; repent and believe in the gospel.”
Mark’s account plainly refers back to the Old Testament.
(Luk 4:17-21 ESV) 17 And the scroll of the prophet Isaiah was given to him. He unrolled the scroll and found the place where it was written, 18 “The Spirit of the Lord is upon me, because he has anointed me to proclaim good news to the poor. He has sent me to proclaim liberty to the captives and recovering of sight to the blind, to set at liberty those who are oppressed, 19 to proclaim the year of the Lord’s favor.” 20 And he rolled up the scroll and gave it back to the attendant and sat down. And the eyes of all in the synagogue were fixed on him. 21 And he began to say to them, “Today this Scripture has been fulfilled in your hearing.”
As does Luke’s. And if you remember your Isaiah, so is Matthew’s —
(Mat 11:4-5 ESV) 4 And Jesus answered them, “Go and tell John what you hear and see: 5 the blind receive their sight and the lame walk, lepers are cleansed and the deaf hear, and the dead are raised up, and the poor have good news preached to them.
John’s Gospel does not use the word “gospel” or “good news.”
In short, the three Gospels that use “gospel” or “good news” all refer to the Old Testament to define the term, and there is nothing in the Old Testament about water baptism. Rather, these passages speak of the coming Messiah or his Kingdom.
4. Is water baptism an element of pistis (the Greek word for faith)? (If you argue that faith implies obedience and obedience implies baptism, then what other acts of obedience are as essential as baptism?)
Of course, not. “Faith” includes faithfulness or obedience, but obedience is a heart of obedience not perfect obedience. My son is obedient to me even if he sometimes misunderstands my instructions and sometimes fails to do as he’s been told provided he has an obedient heart that prompts him to be generally — as a rule — obedient.
There is no one or five or 20 particular acts of obedience that are essential being obedient in the sense of faithfulness or pistis. Converts will only obey as well as they are instructed — at best — and aren’t accountable for bad instruction as babes in Christ. And disagreements about what the Bible requires are disputes among obedient people trying their best to understand across vast language and cultural barriers.
5. What are the essential elements of a real, efficacious baptism? And by “essential” I mean God absolutely will not save you if you miss this element — regardless of your faith, your repentance, or confession. If you miss an essential element, you are without hope.
Well, to me, the essential part is the part done by God. We really can’t save ourselves. Of course, that’s not an element that we do. I find the essential element of baptism that we do in the words of Peter —
(1Pe 3:21 ESV) Baptism, which corresponds to this, now saves you, not as a removal of dirt from the body but as an appeal to God for a good conscience, through the resurrection of Jesus Christ
(1Pe 3:21 NAS) And corresponding to that, baptism now saves you– not the removal of dirt from the flesh, but an appeal to God for a good conscience– through the resurrection of Jesus Christ,
(1Pe 3:21 NET) And this prefigured baptism, which now saves you– not the washing off of physical dirt but the pledge of a good conscience to God– through the resurrection of Jesus Christ,
(1Pe 3:21 NIV) and this water symbolizes baptism that now saves you also– not the removal of dirt from the body but the pledge of a clear conscience toward God. It saves you by the resurrection of Jesus Christ,
(1Pe 3:21 RSV) Baptism, which corresponds to this, now saves you, not as a removal of dirt from the body but as an appeal to God for a clear conscience, through the resurrection of Jesus Christ,
Regardless of translation, Peter plainly puts the emphasis on the appeal or pledge to God for a clear conscience — the subjective intent to be forgiven (appeal) and/or to be faithful (pledge) — which every convert ever has had — even if taught that he was saved before he was baptized. He still asked God for forgiveness and repented/pledged faithfulness. (To argue that these things must be exactly simultaneous with immersion is to miss the point that Peter is making.)
God asks for mercy not sacrifice. He is far more interested in our hearts than our rituals. That doesn’t nullify baptism, but it does tell us that baptism is far more about the commitment that it represents than the mere act of immersion. There is no magic in the water. But a broken and contrite heart, prompted by faith in the beloved Savior, there’s power in that because that’s what God is looking for.
(Psa 51:17 ESV) 17 The sacrifices of God are a broken spirit; a broken and contrite heart, O God, you will not despise.
(Mic 6:8 ESV) 8 He has told you, O man, what is good; and what does the LORD require of you but to do justice, and to love kindness, and to walk humbly with your God?
(Hos 6:6 ESV) 6 For I desire steadfast love and not sacrifice, the knowledge of God rather than burnt offerings.
And so, when a babe in Christ gets the ritual wrong but gets his heart right, God will not hide his face.