William must have died in or before 1806, since his parents, Robert and Jean, named their next son William also.
Sources
"Scotland, Births and Baptisms, 1564-1950," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/XTLX-7JD : accessed 01 Feb 2014), William Anderson, 04 Jan 1803; citing [REFERENCE-ERROR], reference 2:16JQ4C3; FHL microfilm 1042971.
"Scotland Births and Baptisms, 1564-1950," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:XTLX-7JX : 8 December 2014), Jean Mowat in entry for William Anderson, 04 Jan 1803; citing , reference 2:16JQ4C3; FHL microfilm 1,042,971.
Footnotes
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DNA Connections
It may be possible to confirm family relationships with William by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with William: