Thats a good thought Pennines. There is also the possibility of Ireland

. On the 1841 census there is an Alexander Simeon aged 40 born Ireland living in Liverpool. May be some relation
Just to throw some additional thoughts in, his surname could have be transcribed/misheard as Simon or possible Simmon, Simmons to name, but a few. For instance his daughter Margaret was baptised in 1804 under the surname Simmons.
13th April 1806 St Nicholas, Liverpool
Margaret Simmons, Daughter of John Simmons & Jane (formerly
Bell)), His Wife
Born on 3rd March 1806
Abode Newbird St.
Occupation Book Keeper
There is a death of a John Simmons in the Workhouse, Book keeper on 6th November 1821 at St. Johns, Liverpool aged 40. It is possible that this is the record your cousin found to work out his year of birth. Also buried at St. Johns was a Jane Simon aged 50 on the 8th June, 1828.
Definitely a tricky one.
Mo