The Torah is written in the formula of Narrative-Poetry-Epilogue, both on a grand design and in individual stories. For example, on a grand scale, Genesis 1 – Deuteronomy 32 is narrative. Deuteronomy 33 is poetry. Deuteronomy 34 is epilogue. On a smaller scale this pattern follows as well. In the book of Genesis, chapters 1-48 are narrative. Chapter 49:1-27 is poetry. Chapter 49:28-50:26 is epilogue.
In each formula, the poem contains the kernel of importance to the writer.
I suspect a similar rabbinical writing form at work in First Timothy 6. Without knowing if it was intentional, subconscious, or coincidence on Paul’s part, allow the indulgence.
On a wide scale, 6:3-14 is narrative. Chapter 6:15-16 is poetry. Chapter 6:17-21 is epilogue. Verses 3-14 lay out Paul’s main exhortations and concerns. Verses 15-16 are the hymn composed to Christ. Verses 17-21 repeat and conclude Paul’s thoughts.
The hymn is the kernel of importance to the writer. Christ and His exaltation is the great motivation for Paul and Timothy’s lives.
On a smaller scale, verses three through six are narrative. Verse seven is poetry. Verse eight is epilogue. The poetic focus is the central tenet of the passage. Verse eight serves to conclude.