Gregorio appears in the California Death Index as having passed away on 18 November 1956 in Los Angeles. It lists a birth date of 12 March 1874, born in Mexico, his mother's maiden name as Quijada and father's name as Diaz. I've ordered a copy of the full death record from LA County to see what else is there.
In the meantime, I put this information into Ancestry's database and hit a match for Gregorio Diaz in the US World War I Draft Registration Cards for 1917-1918 living in Elbert County, Colorado. This record includes his signature, and states that he was working as a farm laborer for Bench Brothers in Agate, Elbert County, Colorado (as of 12 September 1918 from the reverse of the card). He listed is nearest relative as Ysabel Diaz, at an address unknown. Right now I don't know if this is the same Gregorio Diaz I'm searching for, but the birth date makes me think it may be a match.
A few years earlier, there is a Gregorio Diaz who appears in the US Census in La Junta, Otero County, Colorado, working on the railroad. The census lists his age as 38, which is close to the age of the Gregorio born in 1874. It also says that he arrived in the US in 1907. The whole page shows railroad workers originally from Mexico.
|Source: 1910 US Census, La Junta, Otero County, Colorado|
|Source: DPL, 1915 AT & SF engine at La Junta, CO|
I was not able to find Gregorio Diaz in the 1920 US Census in Colorado. There is a Gregorio Diaz born about 1874 living in Hermosillo as a widower in the 1930 Mexico Census, but again I'm not sure if this person is the same as the Gregorio Diaz who appeared in Colorado or the one from the death record in California.
I'll post a follow up on Gregorio once I receive the death record from LA County or additional information from the Colorado Railroad Museum.