You may find some clues in his pension application and files which are housed at the Louisiana State Archives in Baton Rouge. Their phone number is(225)922-1000 and ask for the research room. They usually have a date of death listed and possibly a location. Sometimes, but not always, a lot of imformation can be gleaned from these pension files. They have both William T. Bennet's Pension information as well as for his widow, Celia Varnado Bennett. This is the link to their website
http://www.sos.louisiana.gov/tabid/581/Default.aspx