The round signs were called "drumheads", as they looked like drums. These signs were hung on the back of a train, generally on the Observation Car, to display either the train's name or the railroad's name. Most railroads (maybe all) assigned names to their important passenger trains; and - at one time - there were hundreds of named trains. This was done for marketing purposes. Advertising material could be created describing the features, amenities, schedule, speed, and prestige of the train using its unique name. After (roughly) 1930 additional shapes were used for the signs, but term "drumhead" was still used.
The Santa Fe Railroad's Grand Canyon Limited ran between Chicago and Los Angeles - via Kansas City and Flagstaff - and provided service to Grand Canyon National Park via a connection at Williams AZ. Travelers could board a sleeping car in Chicago at noon, and two days later arrive at the Grand Canyon Passenger Station at 7 am, only a short walk to the Canyon Rim. The travelers then had all day to visit The Grand Canyon (taking tours, etc...). At 8 pm (13 hours later), they'd re-board the same sleeping car they arrived in (where they left their luggage for the day) and continue their trip to Los Angeles, arriving at noon the next day. Or, if desired, the travelers could stay additional nights, in (say) the El Tovar Hotel - which was owned by the Santa Fe Railroad and run by Fred Harvey Company - and then catch an 8 pm sleeping car back to Chicago; or to Los Angeles; or - via connecting Santa Fe trains - to: San Francisco, Dallas, or Houston. This service lasted until roughly 1962.
The (now) famous Route 66 paralleled part of this train's route from Amarillo TX to Los Angeles.
The original Santa Fe line between Williams AZ and the Grand Canyon is still being used by the Grand Canyon Railway.
The Sunset Limited was re-equipped in 1950, and the rear car carried the neon version of the drumhead. For more information on this train, see the other set of Drumheads at the other end of the passenger car exhibit.
The Southern Pacific Railroad's San Juaquin Daylight was one of the family members of passenger trains marketed under the "Daylight" name. The San Juaquin Daylight ran between Oakland (San Francisco via ferry) and Los Angeles (like the Coast Daylight) but via the San Juaquin Valley. For more information on the other "Daylight" trains, see the other set of Drumheads at the other end of the passenger car exhibit.
Another set of Drumheads are on the other end of the passenger car exhibit.