If the apostle John was the only apostle to witness the crucifixion then why did he not write it in his own Gospel?

he was to have a gift from God to have what to read in The Bible He did. Jesus' arrest and trial are recorded in chapter 18; the crucifixion in chapter 19, which includes this passage: John 19:25-27 - Now there stood by the cross of Jesus His mother, and His mother's sister, Mary the wife of Clopas, and Mary Magdalene. When Jesus therefore saw His mother, and the disciple whom He loved standing by, He said to His mother, "Woman, behold your son!" Then He said to the disciple, "Behold your mother!" And from that hour that disciple took her to his own home. [NKJV] "The disciple whom He (Jesus) loved" was John's way of referring to himself in his gospel.