I can't say I know the answer to this question but here are biblical verses that could be used to argue that eternal life was not a gift from God prior to Jesus' sacrifice on the cross.
Genesis 3:22
22 And the Lord God said, “The man has now become like one of us, knowing good and evil. He must not be allowed to reach out his hand and take also from the tree of life and eat, and live forever.”
Ecc 3:18-22
18 I also said to myself, “As for humans, God tests them so that they may see that they are like the animals. 19 Surely the fate of human beings is like that of the animals; the same fate awaits them both: As one dies, so dies the other. All have the same breath[
c]; humans have no advantage over animals. Everything is meaningless. 20 All go to the same place; all come from dust, and to dust all return. 21 Who knows if the human spirit rises upward and if the spirit of the animal goes down into the earth?”
John 6: 67-69
67 So Jesus asked the Twelve, “Do you want to leave too?”
68 Simon Peter replied, “Lord, to whom would we go? You have the words of eternal life.
69We believe and know that You are the Holy One of God.”
John 4:7-13
7 When a Samaritan woman came to draw water, Jesus said to her, “Will you give me a drink?” 8 (His disciples had gone into the town to buy food.)
9 The Samaritan woman said to him, “You are a Jew and I am a Samaritan woman. How can you ask me for a drink?” (For Jews do not associate with Samaritans.
10 Jesus answered her, “If you knew the gift of God and who it is that asks you for a drink, you would have asked him and he would have given you living water.”
11 “Sir,” the woman said, “you have nothing to draw with and the well is deep. Where can you get this living water? 12 Are you greater than our father Jacob, who gave us the well and drank from it himself, as did also his sons and his livestock?”
13 Jesus answered, “Everyone who drinks this water will be thirsty again, 14 but whoever drinks the water I give them will never thirst. Indeed, the water I give them will become in them a spring of water welling up to eternal life.”
Eternal life is the Holy Spirit given to church age believers. It does not refer to our human spirit that all OT believers received when they became born again. The human spirit makes us to be spiritual - able to comprehend and to know spiritual realities. Eternal life is God sharing His life with us. That happens by means of the filing of the Holy Spirit that is given to all who believe in the church age.
Here is one passage you showed us which holds the clue to what I speak:
10 Jesus answered her, “If you knew the gift of God and who it is that asks you for a drink, you would have asked him
and he would have given you living water.”
11 “Sir,” the woman said, “you have nothing to draw with and the well is deep. Where can you get this living water?
12 Are you greater than our father Jacob, who gave us the well and drank from it himself, as did also his sons and his livestock?”
13 Jesus answered, “Everyone who drinks this water will be thirsty again, 14 but whoever drinks the water I give them
will never thirst. Indeed, the water I give them will become in them a spring of water welling up to eternal life.”
Living water?
Jesus told us what that living water is and we are told when that would begin to happen!
On the last and greatest day of the festival, Jesus stood and said in a loud voice,
“Let anyone who is thirsty come to me and drink.Whoever believes in me, as Scripture
has said, rivers of living water will flow from within them.” By this he meant the Spirit,
whom those who believed in him were later to receive. Up to that time the Spirit
had not been given, since Jesus had not yet been glorified." John 7:27-39
The Day of Pentecost is when that began its fulfillment.
The Holy Spirit is ETERNAL God! He is Eternal life!
We have been given eternal life because Jesus is now long been glorified after He ascended back to Heaven!
OT saints were given 'everlasting life.'
We have both everlasting life and eternal life because Jesus is Glorified and seated at the right hand of the Father!
Words hold meanings.
We need to learn to become exacting with the Bible if we are ever to find ourselves thinking with Christ, not simply thinking about Christ.
When we think with Christ? We are experiencing having the mind (thinking) of Christ!
And, we have been given the mind (thinking) of Christ! (1 Cor 2:16) He is the Word of God! (John 1:1)
Not all use it (thinking of Christ) by walking in the truth... but too many are only knowing 'about' the truth. Only having an academic knowledge of God's Word. Bible memorization only.
Walking in the truth by means of the filing of the Spirit is experiencing eternal life. Eternal to the capacity for us now given to experience on earth. But, simply knowing truth is not the same thing. (Bible memorization) The Spirit must make the truth be living inwardlly in us as an expression of our being in Christ! His thinking on a matter becomes our thinking on that matter.
Walking in the Spirit makes us able to become one with the Truth. Being filled with the Spirit is when truth becomes matter of fact in the sense that our eyes begin to see the world through they eyes of the Lord Jesus Christ. Its as if He is right there with us sharing in the thought.
That is when we will discover He is in us!
"On that day you will realize that I am in my Father, and you are in me, and I am in you."
John 14:20
Mysteries are never simple at first.
grace and peace .....