Jane Marshall posted a message on this BB about Elizabeth and Edward Watterson in 2006:
www.isle-of-man.com/genealogy/messageboard/manx_archive_1.pl?md=read;id=508826

I have looked up the entry Jane refers to, on Findmypast. The 1851 Household transcription has:
Name, Relation, Condition, Se x, Age, BirthYear, Occupation, Disability, Where Born
GAWNE, Thomas Head Married M 47 1804 Joiner Isle of Man
GAWNE, Anne Wife Married F 60 1791 Isle of Man
GAWNE, Catherine Niece F 12 1839 scholar Deaf Isle of Man
WATTERSON, Elizabeth Sister In Law Unmarried F 54 1797 Isle of Man
WATTERSON, Edward St Neph Unmarried M 19 1832 Ship Carpt (App) Isle of Man
WATTS, John Lodger Unmarried M 23 1828 Mariner Liverpool Lancashire
WATTS, Catherine Lodger Unmarried F 21 1830 Milliner Liverpool Lancashire
ELLIOTT, Thomas Lodger Unmarried M 37 1814 Gen Comb Saleman Longton Cumb
ELLIOTT, Anne Wife F 35 1816 Worthenbury Cheshire
ELLIOTT, June F 8 1843 Leamington Warwickshire
ELLIOTT, Susan F 7 1844 Dormington Warwickshire
ELLIOTT, Charles M 2 1849 Liverpool Lancashire
ELLIOTT, Thomas M 0 (6 MOS) 1851 Liverpool Lancashire

RG number:HO107 Piece:2185 Folio:300 Page:29
Registration District:Liverpool Sub District:Islington Enumeration District:
1W Ecclesiastical Parish:Civil Parish:Liverpool Municipal Borough:
Liverpool Address:
31, Spring Place, Liverpool County:Lancashire

In this census Elizabeth is presumably given as Anne Gawne's sister, Thomas Gawne's sister-in-law - but unfortunately Jane couldn't find a marriage for them so didn't know her maiden name.
The unmarried for Elizabeth might just have meant widowed - unmarr at the time, or perhaps she and William didn't marry. I still think it would be well worth your while to look at those two wills, and also the parish register. A place name at the bapt might show whether those other two bapts in Castletown were their children as well.

The "Ship Carpt (App)" for Edward fits in with what you wrote.

I've had a look at the scan and I think that "St Neph" is actually written as Gt Neph (of Thomas Gawne and his wife Anne) although as Eliz is Thomas's "S.in L." probably an error by the enumerator. The "U" for Eliz could be a "W" - hard to tell.

Sue