There seem to be two messages here. One is that Scriptures tell us of the Jesus but they are not Jesus, they are the way we know about Jesus, but atheists and the devil can read and know scripture and do not believe in, do not have faith in Jesus. Eternal life comes through faith in Jesus, in His redemptive cross, in His resurrection.
The NABRE note on this verse states: this may be an imperative: “Search the scriptures, because you think that you have eternal life through them.” Here is the same message with a stronger emphasis on urging them, encouraging them to actually use their devotion, their belief in the Scriptures which contain the message of eternal life to find that they do testify to Jesus and in this way, come to believe in Him.
I personally can testify that daily searching the Scriptures does truly testify to You, Jesus, to all You are, to all You said, to all You did, to Your life lived for me, to show me how to live my life, how to follow You, how to take up my cross daily and trudge up Calvary, how to love even my enemies, how to forgive, how to show mercy and compassion, how to manifest anger and frustration so that these do not consume me and lead me to sin, how to witness to the truth even unto death, how to let our Father do unto me whatever He deems best, how to do whatever He tells You, even if that means drinking the cup that You drank, Jesus. Scriptures unroll for me the panorama of God’s Love over time and space, in the lives of individuals and of His people, from the Garden of Eden to the establishment of His Church and the spreading of his word throughout the world.
But in the end, I must rely on Your gift, Your precious gift of faith, of hope, of Your witness of love in my life to bring me closer to You each day. Only in this way can I get to know You on a personal basis, become Your friend, Your companion, Your ally, Your disciple, Your apostle, Your witness, Your martyr…and thus, from reading testimony, I become testimony. God invites me to become living evidence (not conclusive proof) of a good God. Put simply: to our modern world, the most compelling evidence for God is a life well-lived by those who claim God. (Paul Moser, Evidence for God, 215).
 Scripture texts in this work are taken from the New American Bible, revised edition © 2010, 1991, 1986, 1970 Confraternity of Christian Doctrine, Washington, D.C. and are used by permission of the copyright owner. All Rights Reserved. No part of the New American Bible may be reproduced in any form without permission in writing from the copyright owner.