I think John is correct that the style of cap varied with geography as well as historical era, so the fashions of Western railroaders in the 1950s-1960s aren't necessarily indicative of what was worn in other places and times.
Historical photos of actual Maine narrow gauge engine crews show them wearing either the short, round-topped version of the engineer's cap John describes as more characteristic of the East, ordinary flat caps, or sometimes even broad-brimmed hats.
Here are some examples.
Wesley Glidden and Earl Keefe with WW&F engine No. 4 on the Wiscasset turntable, circa 1930:
Engineer Fred Leavitt, conductor Rob McMullen, and brakeman Clarence 'Sonny' Fairbanks with SR&RL engine No. 17 in 1936:
An earlier Sandy River crew with SRRR engine No. 8 (= SR&RL No. 19):
And an even earlier engine crew on the Monson RR with engine No. 2, the 'G.S. Cushing':
-Philip Marshall