We would know at least one point in time when John was on the Island of Patmos if we knew when the Book of Revelation was actually written. Burton L. Mack (Who Wrote the New Testament) says that...
Because he was a Christian preaching the Gospels. But this history is not sure.
Revelation 1:1 states that the Book of Revelation was written by a person called John, and Revelation 1:9 says that...