Above: Tomb of St John, Ephesus
John, the beloved young man as a staunch disciple, and beloved as well, "the elder" near the end of his life, in a dangerous time and in dangerous places, in a church that was being dispersed throughout the Roman (and pagan, persecuting) world and that was unfortunately embroiled in its own internal disputes. John, faithful witness at the cross and, so far as we know, the only disciple not martyred for his faith.
John's little letter has come to us, courtesy of the otherwise unknown Gaius. John encourages Gaius to stay focused on the mission work, and stay in the truth. Gaius perhaps came to believe through John, but they have been mostly apart since then, so John commends the good things he has heard about Gaius. But he does not use many words, preferring to save his wisdom for a time not long hence when they can share fellowship face to face.
Always with John it is the fellowship of brothers and sisters in Christ that anchors the church, brothers and sisters each with a unique character but each loved, to the end. If John has authority, it is because he has lived that love in all circumstances and among all.