By what means can I break this covenant? I'd like to have a more specific answer than the one given in the text. Is there another text which describes this?
Here are a few more texts. Compare and contrast them to see what the conditions are for life and death. Broken covenant = death.
John 17:3 - And this is eternal life, that they may know You, the only true God, and Jesus Christ whom You have sent.
1 John 5:12 - He who has the Son has life; he who does not have the Son of God does not have life.
1 John 3:9 - Whoever has been born of God does not sin, for His seed remains in him; and he cannot sin, because he has been born of God.
Ezekiel 18:20 - The soul who sins shall die.
Romans 6:23 - For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.
John 5:24 - 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.
Luke 13:27 - Depart from Me, all you workers of iniquity.
Matthew 19:17 - But if you want to enter into life, keep the commandments.
Romans 6:8 - Now if we died with Christ, we believe that we shall also live with Him,
Romans 6:3-4 - Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life.