The glaringly obvious suddenly occurred to me. If John Isaac Wilson became a naturalised US citizen, then the relevant papers would probably reveal his place of birth.
However, what I have found is a string of lies ... or he is not related to Arthur.
On 27 May 1922, Arthur did indeed arrive in New York on the
Mauretania, with the intention of staying with - I quote from the manifest - '
sister, Mr. & Mrs. J. Wilson, 123
0 Overlook Street, Mt. Vernon, NY'.
123, not 1230, Overlook Street was occupied by John Wilson and his wife, Isabell(a) from at least 1920. This John was indeed formerly known as Jacob or Jack Isaacs. But in every census and in his Declaration of Intention (to become a US citizen) he claimed that he had been born in London on 18 Sept 1877.
Jack Isaacs and Isabell Shuman (Schumann) were granted a marriage licence in New York on 7 Sep 1908. In 1910, they were still living in Manhattan but under the surname Wilson.
Isabella's repeatedly lied about her age. In the censuses with Jack/John, she admits to being a couple of years older than him. In reality, she was recorded as a seven-year-old with her parents in the 1870 census.
When registering for the draft in 1918 in Mount Vernon, John signed John Irving Wilson.
What other sources do you have that link John Isaac Wilson and Arthur Isaacs?
Justin
UPDATE: The marriage record here
https://www.familysearch.org/ark:/61903/1:1:24C7-KP9 confirms that Jack's parents were Goodman and Jane Isaacs. But I find it highly unlikely that he was born on London.