I think you have linked to the wrong Wiiliam ELDER.
The one you want is probably this one. He is a cousin.

William ELDER the son of Alexander ELDER & Agnes SWINTON was according to Church of Scotland Parish Records for Dysart, Fifeshiee was born on 11 Mar 1791 and baptised at Dysart on 22 Mar

The Kirkcaldy Church of Scotland Parish registers give the birth of his sister, Christina on 17 Sep 1801
In 1825 a marriage Licence Bond between her & John LUXMORE
states she was of the Parish St Philip Liverpool & he was of Plymouth
(see: https://homepages.rootsweb.com/~mwi/che1825f.txt or FHL Film No 1894493)