A train running as a scheduled train wouldn't have classification signals. Classification signal lights on a locomotive would be white if the train is an extra or green if it's a scheduled train with a following section or sections.... In the "classic" passenger train era, passenger trains often had more passengers than could fit in one train, so would have one or more "sections" - separate trains - following five or ten minutes behind (or sometimes ahead of) the scheduled train. A train like the GN Empire Builder or NYC Twentieth Century might run in up to 10 or 12 sections during WW2.
Well into the diesel transition era railroads used flags to denote classification during the day, as they had going back to before electric lights. BTW engines generally didn't use headlights during the day until into the fifties, and small classifications lights wouldn't be seen well during the day anyway.
Trains magazine has a section giving some more information.
Marker lights or flags indicate the end of the train. All trains, even an engine moving by itself outside of a yard area, would have to show red lights or flags on the rear indicating the end of the "train". Caboose marker lamps would normally show red forward and back, and green to the side IIRC.
Note that on engines and cabooses "flags" were not always literally flags, they could be flag shaped items made of metal for durability, made to fit the flag holders on the engine or caboose.
For the model locomotives, I suppose white would be best for a freight engine, since freights often ran as extras. For a passenger engine, no lights or flags would probably be most appropriate.