Perhaps you could be clearer and explain what "belief in Jesus" means to you.
If I am a Jew living before the cross, what exactly do I have to believe about Jesus to have life?
Can I then considered myself dead to the Law of Moses and still be considered to have life at the end of my lifespan?
...Belief in Jesus means for people living now, after Jesus 1st advent. Is that we have a clear written image of who God had promised to send, this person is is know in English versions of The Bible as Jesus.
...At the actual time of Jesus being physically alive on earth. The Jews at that time had an actual physical person who was preforming miracles that only the promised Messiah was able to do.
Then they brought him a demon-possessed man who was blind and mute, and Jesus healed him, so that he could both talk and see. All the people were astonished and said, “Could this be the Son of David?”
...So they had The physical person of Jesus to believe in, who was the only person, to be able to do the miracles prophesied in The Tanakh that The Messiah was going to do.
...Jews before the advent of The Messiah, Israel still had the promised to come Messiah, to believe in for Eternal Life. They did not, the farther history went back, have an actual name but still they had knowledge of a promised Messiah.
Your father Abraham rejoiced to see My day, and he saw it and was glad.”
...With all that said, it is for past, present and future people belief in The messiah for Eternal Life.
...That in The Messiah is the life of God. Now we know Jesus is the resurrection and the life (The Life of God), the promised only begotten Son of God, The promised Messiah from the prophecies of The Tanakh.
...So when verses from John say belief in Jesus gives a person Eternal Life. The belief is that this person Jesus is the resurrection and the life and to believe that He, Jesus is actually who He says he is, is to believe in Jesus.
...That is to believe this is the way to receive God's free gift of Eternal Life by Belief in Jesus and not to believe Eternal Life is received by other means repentance, following the law, obedience, saying a prayer, believing a gospel. etc...
John 5 24 states when a person believes in Jesus they at that moment of belief, cross over from death to life. The verse does not say the believer will eventually cross over from death to life if they believe and follow the law. etc..
“Most assuredly, I say to you, he who hears My word and believes in Him who sent Me has everlasting life, and shall not come into judgment, but has passed from death into life.