It seems to me that the "elect" are chosen for God's purposes, whatever or whenever that might be in history, and by God directly or through the Holy Spirit.
Mark 13:20 (Jesus speaking of the tribulation) “If the Lord had not cut short those days, no one would survive. But for the sake of the elect, whom he has chosen, he has shortened them."
Mathew 24:22 (Same here) Unless those days had been cut short, no life would have been saved; but for the sake of the elect those days will be cut short.
So I conclude that God directly and personally favors a small number for his purposes whatever they may be.
I don't feel this is "picked" to be saved. Though of course, as God says to Moses, “I will have mercy on whomever I will have mercy, and I will have compassion on whomever I will have compassion.”
I feel elect are a group picked to serve God's purpose on earth, are among us today, and that probably most of these have not a clue that they are furthering God's plan for mankind.
To me Paul was most certainly one of the elect. We are told of what he was doing when he was doing his own will with his own passion. Yet he was struck down on his way to do his own thing and he was the most educated in the Hebrew scripture of all the New Testament writers and penned most of the New.
I too believe those chosen as Paul describes in Ephesians 1 before the foundation of this world (age) will be in place when they are called upon to testify as was demonstrated in Chapter 2 of Acts. And what took place in Acts 2 was already foretold in Joel. That is instructive to me that at minimum the elect would need to have at least a cursory understanding of the so called old or the Hebrew script. Paul does say that ICorinthians 10:11 we have been given the script as to what would be to end this flesh age.
I also believe that Christ is the standard that any of the 'elect' will follow as is stated in John 3:16.