I was able to locate a nice writeup on this museum from the City of Montague website (link below) that highlights this railroad museum and its relocation to its current site. It reads:
A BRIEF HISTORY OF MONTAGUE’S RAILROAD
When the Central Pacific Railroad decided to build its line through the county to connect with the Oregon and California Railroad in Ashland, Montague was chosen to be the next town north of Gazelle. In January of 1887, L.D. Norton was sent to lay out the town site on land that was donated by the Prather Brothers and C.C. Webb, a half section each.
The tracks were completed through Montague on February 8, 1887. As was the tradition of the Pacific Improvement Company, a huge promotional campaign was conducted and an excursion train from Oakland brought up to Montague to auction off lots in the new town.
The depot was built in five weeks and, according to the March 31, 1887 edition of the Yreka Union, it was "a Magnificent structure of redwood, even to the shingles". In 1906 the platform was enlarged to 40 feet and in 1916 the office and freight house were enlarged, and another waiting room added.
Montague became an important shipping center soon after the cattle corrals were built. In 1888, Yreka built a short line, the Yreka Railroad Company, to connect with Montague. Montague was incorporated January 25th, 1909.
The Southern Pacific Railroad Depot's last day was officially October 15, 1977, after ninety years of service. The Southern Pacific Transportation Company donated the depot to the City of Montague in 1978 with the provision that it be removed from their property. It was moved to its current site in 1978. The museum had a facelift (new roofing, paint, electricity and more) in 2003 and 2004 and is now set up as closely to the original as possible.
For more information on Montague and its history, a book titled "The Siskiyou Pioneer", the Montague issue, is available at the depot gift area.
I'm in the process of trying to locate an old map of this city so I can find out exactly where this railroad depot was formally located. I'll update the coordinates if/when I do.