The census links were posted so that everyone could see the details without everyone having to search.
You haven't really answered the question I was asking. Not being listed as son's next of kin in 1924 doesn't confirm that the father is alive or dead so doesn't help to find his death. We need to work forward from the last sighting. Is the 1911 census the latest record of him, and his wife, found?
What about the son's marriage (when?)- what's his father's occupation then and is he listed as deceased?
How were you able to rule out the 1941 death?
Are you related to the Walker family? did anyone keep in contact with William? or is there any indication that he disappeared or emigrated?
Unfortunately he might appear in records just as William Walker making him more difficult to pin down.