I'm afraid some of the information on the webpage regarding Alexander Dalziel is factually incorrect.
Before trying to find your Alexander Clark thought it best to try and figure out the 2 women referred to i.e. sisters Agnes and Elizabeth Clark as I was intrigued as to why they would have a different surname to Alexander Dalziel.
First of all, the 2 women weren't sisters (they were mother and daughter) and Agnes' maiden name was actually Waddell (or Waddel - spelling varies from document to document).
Stoneyburn House was originally the home of the Waddell family - Alexander Waddell and wife Elizabeth Greenhorn had just 2 daughters - Agnes b.4/9/1838 Whitburn and Jane b.30/9/1840 Whitburn.
Agnes Waddell married Thomas Clark, a doctor, on 22/9/1865 Whitburn.
Jane Waddell married Alexander Dalziel in 1876 - they had no children - in 1881/1891 Jane is living at Stoneyburn House with her widowed mother and in 1901/1911 lived there with husband Alexander Dalziel.
Jane Dalziel (nee Waddell) died in 1922. Alexander Dalziel did indeed die in England but your year is incorrect. He died 13/8/1924 and his will was proved in Scotland on 17/9/1924 - address is given as Stoneyburn House, afterwards Hillside, Loudwater, Bucks. (his death entry shows this to be in the Wycombe, Buckinghamshire registration district).
So, after Alexander Dalziels' death the house became home to his sister in law Mrs. Agnes Clark (thus returning to her family home) and when she died there 22/2/1939 it passed to her unmarried daughter Elizabeth Clark b.12/5/1866 (shown as Bessie on early census records). Elizabeth Clark died 6/1/1952 in Bangour Hospital, Broxburn - her usual address given as Stoneyburn House, Stoneyburn.
Having clarified all that I then looked at Agnes Waddel's husband Thomas Clark who had to be whom your Alexander Clark connected to. Thomas and Agnes married 22/9/1865 Stoneyburn, Whitburn - his parents are shown as Alexander Clark, Landed Proprietor (deceased) and Lillias nee Scrimgeour (deceased).
Thomas Clark was born 27/10/1822 Bathgate, parents Alexander Clark and Lillias Scrymgour. Found baptisms for 3 siblings i.e. Alexander bp.22/11/1817 (mothers name spelt Scrimzier?), George b.24/2/1820, Lillias b.12/8/1823 plus census shows there were 3 more - Ann bc.1816, Mary bc.1826 and James bc.1829. However, the 1841 census (when ages rounded down and only shows whether they were born in the county or not) shows Alexander Clark bc.1771 not born in West Lothian, Lillias bc.1791 not in West Lothian, dau. Ann bc.1816 not in West Lothian but all the children after were born in Bathgate where they were living. 1851 census shows Lillias now widowed and living with her is a brother William - this time it shows she was born ca.1784 Polmont, Stirling and her brother ca.1786. Think that her ca.birthyear is incorrect in 1851 as found William Scrimgeour's baptism 23/9/1785 Polmont and her's as Lily b.4/8/1790, bp.11/8/1790 Polmont - their parents being a George Scrimgeour and Lily Black. William died 2/7/1858 West Inch, Bathgate aged 76, and confirms his parents as George (farmer and gardener (dec'd) and Lillias nee Black (deceased) and the informant of his death was Alexander Clark, nephew i.e. your ancestor.
Unfortunately, cannot find where/when Alexander Clark and Lillias Scrimgeour married, nor the birth/baptism of eldest child Ann. Nor do we know where Alexander was born ca.1771 (definitely in Scotland, but not in West Lothian according to 1841 census).
So, jim1 is correct and your Alexander Clark is indeed the one bp.22/11/1817 Bathgate, son of Alexander Clark and Lillias Scrimgeour.
Thank you for posting this - I have enjoyed looking into this family this evening.
Annette
