Amen! John 1:12 is attached with "a personal surrender to Him" in Vine's definition. John 1:12 - But as many as received Him, to them He gave the right to become children of God, to those who believe in His name. There is the personal surrender to Him. When we choose to believe in/place faith in Jesus Christ for salvation (Acts 16:31; Ephesians 2:8) we are entrusting our spiritual well being to Christ, along with placing confidence, trust and reliance in Him for salvation. That would be a personal surrender to Him, resulting in justification (Romans 5:1) and that is the ROOT of salvation.
The FRUIT of salvation would be living by or "out of" faith, as we see 2 Corinthians 5:7 attached with "a conduct inspired by such surrender" in Vine's definition, which reads - For we walk/live by faith and not by sight. This is our continued walk with the Lord by which by or "out of" faith believers bear fruit/produce works. So faith in Christ is the ROOT of salvation and "a conduct inspired by surrender" which FOLLOWS and produces good works would be the FRUIT. Pisteuo is mixing cause and effect and the end result is works salvation.