This is a personal letter from John to Gaius. All instances of "you" and "your" refer to Gaius and are singular. (See: [[rc://en/ta/man/jit/figs-you]])
This refers to John, the apostle and disciple of Jesus. He refers to himself as "elder" either because of his old age or because he is a leader in the church. The name of the author can be made explicit: "I, John the elder, am writing." (See: [[rc://en/ta/man/jit/figs-explicit]])