In Amos 5:4, God through Amos said, Seek Me, and live! He is implying eternally. If we seek God, we will live. Now eternal life does not especially have to do with duration, because living the kind of life that God wants us to live is an enjoyable life. Just because one lives eternally does not mean that they are going to be enjoying life.
When Jesus Christ says that eternal life is to know God, He is implying quality of life as primary and length of life as secondary. He is implying that, if we begin now to know God, the abundant life already begins and we begin to experience the kind of life that God lives - the only kind of life that is worth living eternally (that is, days without end).
We find, then, that this kind of life comes from an intimate relationship with God - implied by the word know. Sexual connotations. Adam knew his wife Eve, and suddenly she had babies. So eternal life comes about as a result of experience - intimate experience - of living with God.
