Excellent. These are the kinds of discussions I really like.
There are two 'types' of faith. Man's faith - God's faith. Faith is simply believing and doing what you understand to be true. When you believe and do things based on Man's faith - you sin. When you believe and do things based on God's faith - you are righteous. The difference between the two is absolute truth. Man's faith is not based on pure truth. God's faith is based on pure truth.
Jhn 4:10
Jesus answered her, “If you knew the gift of God, and who it is that is saying to you, ‘Give me a drink,’ you would have asked him, and he would have given you living water.”
God's faith can only be given to us. We cannot take it, or make it up ourselves. It is a gift from God. God's faith is given to us in order to understand the truth. Truth is only understood through faith.
Jhn 14:15-17
“If you love me, you will keep my commandments. And I will ask the Father, and he will give you another Helper, to be with you forever, even the Spirit of truth, whom the world cannot receive, because it neither sees him nor knows him. You know him, for he dwells with you and will be in you.
The Spirit is given to us in order to distinguish what is truth - and what is not. That is why those who are void of the Spirit cannot understand the truth - neither can they contain it or use it. When the Spirit comes into the believer, then that person now has the ability to know truth and do truth - this is called true faith.
This is why it is impossible to have truly believe in Christ without the 'gift' of God - which is the faith of God - given to us by the Spirit of God.
The Spirit of truth dwells in us by that faith.
Gal 3:2-3
Let me ask you only this: Did you receive the Spirit by works of the law or by hearing with faith? Are you so foolish? Having begun by the Spirit, are you now being perfected by the flesh?
So, the Spirit of truth is Who comes and dwells in us containing the truth of God. In that we live and walk by faith. Its true faith because it comes from understanding the truth of God, which is only because of the Spirit of God.
Jesus was telling the woman at the well that the "gift" of God, which is given by the Spirit of God, would be the living water. Faith is that gift, and we know that the faith we have is true when we see the life it gives in us and from us.
To bring this back home, you are correct - truth is what the 'well'(structure) is because it is the Spirit of truth. Truth is the qualification of the faith of God. If a persons faith is not 100% true - then it is not God's faith. From the 'well'(structure) of truth, we have the 'welling'(flow) of faith that is in the person and flows from the person.
Faith is the manifestation of what is inside a person. False faith is not life giving. True faith is life giving. It is by true faith that we live.
Rom 1:17
For in it the righteousness of God is revealed from faith for faith, as it is written, “The righteous shall live by faith.
Gal 2:20
I have been crucified with Christ. It is no longer I who live, but Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me.
Heb 10:38
but my righteous one shall live by faith,
and if he shrinks back,
my soul has no pleasure in him.”
I don't think there are two types of faith. God is faithful. He gave us a measure of faith when he made us, according to his will, for his purpose. Certainly God gives growth. Peter speaks of a level of faith, 'those who have obtained a faith of equal standing with ours" ie. a faith of standing equal to an apostle. 2 Pet. 1:1 When Jesus spoke of faith it was always 'your faith' or 'their faith'. He was looking for faith. Found faith. Mt. 8:10 And he said will he find faith when he returns. Luke 18:8
But re. water, the water is the word of God.
Apollos watered the church. He didn't water the church with faith. He watered the church with the words of God, specifically the words Jesus gave us when he said,
John 17:8
for I have given them the words which thou gavest me, and they have received them and know in truth that I came from thee; and they have believed that thou didst send me.
Amos said there would be a famine on the land; not a famine of bread, nor a thirst for water, but of hearing the words of the LORD.
Amos 8:11
“Behold, the days are coming,” says the Lord God, “when I will send a famine on the land; not a famine of bread, nor a thirst for water, but of hearing the words of the Lord.
We know branches wither for lack of water. We know when the unclean spirit passes out of a man he passes through waterless places.
Matthew 12:43
“When the unclean spirit has gone out of a man, he passes through waterless places seeking rest, but he finds none.
So shall it be with this evil generation. They search for the truth in waterless places. It might be they go to church but the church has become waterless. Or they might turn on the TV in search of water, but they find no water. The word of God can not be found anywhere.
They're not looking for faith. They are looking for truth.
When Peter wanted to warn us there will be false teachers, he called them 'waterless' springs meaning there was no water in them ie. the word of God is not in them. 2 Peter 2:17
Jesus said, "He who believes in me, as the scripture has said, ‘Out of his heart shall flow rivers of living water.’” John 7:38
The whole idea and God's purpose is to make us like our Master. Christ is the fountain of living water, and we become fountains when we believe in him.