I disagree with the analogy. That leans towards the one-nes pentacostal's idea.We cannot figure it out with human mind. There are three distinct beings, each in existance at the same time. The trinity is three in one, not the one in three forms, or functions, etc.
Jesus prayed/communed with the Father. The comfortor, Holy Spirit, came after Jesus left. There has been a presence of God on the earth with man all along, just in three different persons. God walked with Adam, etc., Jesus walked with man, the Holy Spirit occupies the temple, which is man.
We can't understand a God that has no beginning and no end, let alone a God in three persons. But we will some day.