The earliest date the OED has for “Anglo-Manx” is 1934. They do not even pick up on the title The Vocabularly of the Anglo-Manx Dialect published in 1924.
In 1895, Brown felt that “I have an idea that Mr. M[oore]’s new book will show plainly that we have arrived at the last squeak of the Manx language proper.” He continued in his letter to Egbert Rydings who had written short stories in Anglo-Manx:
“So I think what we have now to do is to make a new start, making Anglo-Manx dialect the basis. In its turn this will probably become obsolete, but meanwhile the catastrophe will be deferred by your stories, and, perhaps I may add, mine.”
However, I can trace it now to John Rhys writing in 1892 (not that much further in this case) in “Manx Folk-Lore and Superstitions. ii.” Folklore iii.1 (1892): 74–88. On pages 76, fn. 1 and 85 to be precise and it is used in a linguistic and not an ethnic sense.
The history of the term certainly calls for further research.
‘The Light Blues Stroke’ Sydney Swann from ‘Rowers of Vanity Fair’, Vanity Fair 1912.
The 2012 Olympic’s were heavily touted as the games when the Isle of Man would finally break a 100 year absence from the top step of the podium on the world stage; even if the eventual record breaker was not the expected Mark Cavendish, and was instead the underrated Peter Kennaugh. In 1912 Sydney Swann, a member of the Leander Rowing Club who stormed to victory in the final of the men’s eights, was the pioneer ‘Manx’ winner of Olympic gold. Yet any connection with the Isle of Man was purely accidental being born whilst his father was, for a short spell, curate at Sulby, Isle of Man.