If it may help you:
New Mexico death records on familysearch.org show that:
John Thomas Higgins died 13,Dec,1935 in Catron County.
His parents are given as Patrick S.Higgins and Perfecta Sanchez.
He was born Feb.17,1885 probably in Socorro County,which later became parts of Catron County.
The 1900 census of Frisco,Socorro,NM shows:
Higgins,Perfecta-born Apr.1850;50;married 37yrs;16 children born,12 living;born NM,parents same,owner of a farm
daugher-Barbara-born Mar 1881;19;born NM,father born Ireland,mother born NM;dress maker
daughter-Ines-born June 1883;16
son-John T.-born Feb.1885;15
daughter-Rosy T.-born July 1887;12
twins-Emmett and Lissie born Apr 1890,age 10
Patrick Higgins was counted in San Marcial,Socorro,NM-born March 1833;67;married 36yrs;immigrated 1852;born Ireland,parents same;famer
Perfecta is listed with him,but that does not mean she lived there necessarily;also in the home with Patrick,is married daugher Jennie Montoya,born July 1870;29;married 7yrs;2 children. No spouse or children are with her.
Patrick Higgins was enumerated in the Veteran's census of 1890, in Socorro County, having served in two different infantry units in the Civil War between Apr.1861 and Sept.1866.
You might want to wander about in the NM death records here:http://pilot.familysearch.org/recordsearch/start.html#p=coll...
There are many records for this family;you can search including parents names etc. with the "advanced search" on the bottom left, but be liberal with spelling;Perfecta is spelled badly on several etc.
Found this bit for the brother of John T.:
"Daniel Higgins, pioneer of Glenwood, Catron county, died Sunday at San Diego, Calif.,he was visiting relatives. He had lived in Catron county throughout his life where he was engaged in ranching for many years and also had business interests at Glenwood where the family is well known. News of his death came in a message from his son Nick Higgins."
In the 1930 census "Johnny Higgins" and wife Sarah live in Mogollon, with children Sybel age 8 and Johnny Jr.age 1; I see a death record for a daughter "Margory" who was born in 1922 and died in Silver City in 1924.