On page 740 of "The Johnson County Kansas Cemetery Index", published in 1983 by the Johnson County Genealogical Society and Library, Inc. in Spring Hill Cemetery
Brown, Sarah J., b. 1851 d. 1950
W Thomas, b. 1847 d. 1929
J. W., b. 1857 d. 1922
I think J. W. may be your man. But you will have to find an obituary to figure out who he is. Best bet will be to search the microfilms of "The Spring Hill New Era" newspaper. The films are available for interlibrary loan from the Kansas State Historical Society to your local library or LDS Family History Center. You can search for the microfilm numbers at this link. Note that the KSHS will only send two films per request.
In the 1920s the obituaries should be on the front page and the paper is a weekly. So it could take several hours of searching to find the obituaries. The 1950 obituary may not be on the front page.
You may want to visit this link to the USGenWeb page for Johnson County, KS and contact the cemetery coordinator. I think she has a contact with the folks who hold the cemetery records. They may be able to provide a death or burail date, which will simplify the obituary search.
If you get the death dates, let me know and I will take a look at the microfilms here at the county library.
I just took at look at www.rootsweb.com and found three gedcoms for William Thomas Brown and his wife Sarah Jane Marquis. William died 21 Jan 1929 and Sarah died 2 Dec 1950. So I will take a look for their obituaries. You might want to take a look at the gedcoms and contact the posters. Search from the top left boxes on the main page, then select the WorldConnect link, and scroll down to the bottom of the page and enter the spouse's surname and year of death. I would search on Sarah name as there likely will be fewer hits than on Thomas W Brown.
Overland Park, KS