I do think, that I understand what you are putting on the table, but I do not think that you are understanding what I am putting on the table, such as, John 17:2, or you would not be asking who Jesus gives eternal life to, and who he does not give eternal life to.
Yes, God did choose an elect people, and they are the ones that he draws, calls, and regenerates to a spiritual life. God gave mankind the freedom to choose how he wants to live his life here on earth, and all of mankind choose not to seek God. God, then, choose an elect people out of "those that choose not to seek him" and regenerated them to a spiritual life, so that, those he regenerated, would seek him.
Yes, God "did not choose", as his elect, all of mankind, but only choose a portion of all mankind out of those that would not seek him. I do not understand why God did not choose all of mankind, as his elect, because God's ways are higher than my ways. I have many question to God, as to why he does and does not do things, but he chooses not to reveal the answers ro me.
God regenerates everyone that he regenerates in the same manner, whether they are newly born babies, people in the Old testament, or people today, and that is by the indwelling of the Holy Spirit. Isaiah 63"11, Then he remembered the days of old, Moses, and his people, saying, Where is he that brought them up out of the sea with the shepherd of his flock (sheep=God's children)? Where is he that "put his Holy Spirit WITHIN him? All of the Old testament saints responded to the call, because they had been born again, with the indwelling of the Holy Spirit, the same as do those that respond to his call today.