there are 4 Graves entries in the Manx telephone directory (on line) including one with the initials T.J.

May I ask where your information come from ? - why I ask is that the 1861 census has 2 Thomas J. (Joshua )'s both unmarried (one aged 14 , the other 49 who was to die 1877 - however if you have lost a generation (possibly by confusion of 2 T.J's) your names fit in with John James of Peel - his parents being Thomas Joshua and Elizabeth Cottier