Pamela,
I found an interesting newspaper archive site. It has a lot of gossipy mentions of the various "doings" in the local parts of New Mexico. (I'll add a sample of the type of items I'm referring to -- but I'll leave it to you whether you'd like to delve more deeply into this)
https://newspaperarchive.com/tags/john-rice/?pr=10&psi=66&pci=7&ndt=by&py=1890,1880&pey=1899,1889/
There is a link near the newspaper descriptions that say "Subscribe to View this Image" -- but I was able to click directly onto the image and it took me to the newspaper and the article, so I'm not sure why it says that.
I do have the impression that there might be more than one person in the area named John Rice, so it's hard to know if any particular mention is about YOUR John B. Rice. At least one snippet about MRS. John Rice mentions Watrous, and another about John Rice mentions Socorro (which is very close to Magdalena, where your widow Lois may have lived at one time). Incidentally, Las Vegas (where some of the articles are from) is a town in New Mexico, not the famous city n Nevada, and it's not too distant from Watrous, New Mexico.
https://newspaperarchive.com/tags/john-rice/?pr=10&psi=66&pci=7&ndt=by&py=1890,1880&pey=1899,1889/
THE DAILY OPTIC by R. A. Kistler December 24, 1891 (Las Vegas Daily Optic)
Up Country Notes
"Mrs. John Rice has been quite sick at Watrous, is now recovering."
(Saturday, March 7, 1891, Las Vegas Daily Optic)
THE DAILY OPTIC
-ON THE STREET-
"A birthday party, with which John Rice had something to do, took place at Watrous, last evening." (That's literally the entire thing.)
This next article was interesting, and was printed in the Las Vegas New Mexico Optic, but was about an event in Little Rock Arkansas, and was likely not about the John Rice you're looking for.
Las Vegas Daily Optic April 4, 1888, Las Vegas, New Mexico
He Loved Another's Wife. Little Rock, Ark., April 3
"Yesterday near Wittsburg, Amos Sharp shot and killed John Rice, who had become infatuated with Mrs. Sharp, and had been annoying her with his attentions. Rice's wife was a witness of the killing, Sharp suddenly entering the house and shooting Rice without a word. Sharp made his escape."
There were pages of newspaper links, and I only looked at a few of them, but maybe one will have a clue for you. I searched for the words "John Rice" and focused the search to the years from 1880-1900.
Reba