Dietz, Adlake, Dressel, & Armspear are probably the most common RR lanterns. Here are a bunch of barn lanterns I had hanging from my porch at my old house. I don't think I paid more that $10 each for them and some were bought in box lots of 3 or 4 at auctions for $10 for the whole box. They are fun to collect but don't expect to get rich.
NH.....IIRC, I think I heard that story on the History Channel one time, and asked my dad about it. Something about the railroaders hanging the lanterns outside of the brothels so they could be found.
I do know that the red lanterns were also used on the cabooses, just like the same as red taillights on a car. Once they got away from the red lanterns, they went with battery operated lights. I do know the red lanterns were used also to signal for a stop.
I still have all of dad's battery operated lantern, and believe it or not, but one lantern still has the "D" Cell square battery in it, and that lantern was up in my mom and dads closet, when dad retired. Dad gave me the lantern about 27 years ago. Dad retired at 65 and passed away at 95, two years ago, so that battery is 37 years old roughly, and it still works.
I have three of the gas lanterns. Two with red globes, and one with a white globe. All three are different makers, and I just looked and darned if not one of them is a Dietz. One is a Handlan and has a red globe, the white globe lantern is an Adlake, and the other red globe is The Adams & Westlake Co. All three are NYCS lanterns.
The battery lanterns are Justrite, Adlake, and the Star and Headlight Co. And the rear caboose light that is battery is also a Star and Headlite co., but it is now shortened to Starlite.
My brother-in-laws father was the head of the Wrecker crew. He was the first one called out in an accident. He had a hell of a collection of lanterns (maybe 75+) and railroad locks and keys. He had three 4x8 sheets of plywood in his basement with nothing but railroad locks and keys. He was also an old time railroader and was my dads age. Sadly he committed suicide at 89 years old. My BIL hooked up with an auctioneer when it came time to clean out the house, as my BIL just didn't want to mess with things. He told the auctioneer to write him a check for everything in the house, then whatever he could sell it for to go ahead as he had no interest in it. There were also 3 complete sets of Passenger car/dinner car place settings. By that I mean that there were like three complete settings that would serve maybe 20 or so people. So you're looking at like 60 plates, 60 cups, 60 saucers and so on. All of this was also NYCS items. My BIL got a grand whopping total for everything in the house and garage and all the RR memorabilia of $5000

He practically gave it all away.
I don't have a lot of items from when dad was on the RR. I do have his keys and one lock I think. I have his Hamilton RR Pocket Watch that is in like new condition, then of course his lanterns. Back in the day when dad started on the RR, he was required to have a watch, but couldn't afford one, so the Trainmaster pulled him aside, told him to take this note to the local jewelry store, and get a watch. I think dad said this was back sometime in the late '30's. Dad got his watch, and I think he had to pay back something like $.75 a week until it was paid off.

Even today, the Hamilton's are not worth what one would think they are. You'd have to have a hundred of them to probably equal a Rolex in cost, but the story about paying for it is priceless.