"Hath God cast away his people?"
Brakel does not let that question be solved by giving the word "people" another meaning straightaway. He says explicitly that he is speaking of the Jewish nation.
From rejection to expectation
Chapter 6 first treated the transition from Jews to Gentiles in church history. Then Brakel raises the objection: is that rejection final? His answer is no. He expects that the Jewish nation will still acknowledge that Jesus is the promised Messiah.
He does not mean only Judah and Benjamin. He speaks expressly of the nation in the broad sense and also treats the dispersion of the tribes. His historical reasonings are seventeenth-century and must be read as such, but his theological intention is clear: the dispersion does not make God's future dealing with Israel impossible.
Romans 11 as first main text
Brakel begins his proof in the New Testament with Romans 11. Paul himself opens with a denial: God has not cast away His people. Then follows the tension of stumbling, acceptance, provoking to jealousy and life from the dead.
For Brakel it is especially important that Paul speaks of a future movement. The present hardening is not the last word. The "until" of Romans 11:25 therefore receives eschatological weight.
No automatic salvation
Brakel's expectation of Israel does not mean that descent in itself saves. His whole covenant doctrine has precisely distinguished external relationship and faith. The future he expects is conversion: acknowledgement and confession of the Messiah.
Why this question also concerns the Gentile
Paul does not only tell the Gentile believer information about Israel's future. He corrects an attitude. The question about Israel thereby becomes a mirror as well: what does grace do with our dealings with those whose covenant history preceded us?