Are you sure that William Brown died in 1954?I found his wife in the 1930 census, listed as a widow.Maybe the 1954 death was his son William?
1930 U.S. Federal Census > Texas > Tarrant > Fort Worth > District 19
601 Zenith?? Main (rents $16)
Phelbie Brown, head, white, 49, widowed, reads, writes, b TX, father b AL, mother b TX
Charlie, son, white, 24, reads, writes, b TX, father b Germany, driver for cab co
Robert, son, white, 22, reads, writes, b TX, father b Germany, chauffer (sic) for cab co
Horace, son, white, 18, reads,w rites, b TX, father b Germany, store salemsan
Billie, son, white, 12, attends school, b TX, father b Germany
John, son, white, 10, attends school, b TX, father b Germany
Nellie, daughter, white, 6, attends school, b TX, father b Germany
Goodwin (no first name listed), lodger, white, male, 45, single, he and parents b TX, laborer (ranching)
Since Nellie is 6 in 1930, it is likely that William died between 1923 and 1929 (The census date for the 1930 census is 1 January 1930).You might want to contact the Texas STate Library and ask them to look up the death date for William.You can email them at: email@example.com
With a death date, you can order his death certificate, which should give the names of his parents.
Youmay also want to contact the Tarrant County courthouse and find out if they have a will or probate for William on file.