Moving a caboose is a major deal. It costs a lot of money to have an inspection and pass it. You cannot move a car over the rails unless it’s been gone over with a fine tooth comb. Then it costs - per mile to have it moved. Once moved you have to pull it off onto a spur and hopefully you can keep it there or somehow get it moved to its permanent place.
BTW thank you for the information about the railroad museum. I looked it up. They have more than 100 locomotives and cars there. That’s astounding. I’m curious as to why it is located there. The website didn’t seem to have that information.
I would figure that most rail cars/cabooses, etc., would be on a side rail in some abandoned railway yard, but what do I know? Anyway, my assumption would be that a car is simply picked up by crane and placed on a flat bed for moving. I can see how that’s expensive. Strasburg RR still runs on a two or three mile track as a tourist train, although some of the local Amish use it to go from field to field. I forget the history of the place, but being a part of Pennsylvania RR, there were plenty of stations and enthusiasts about to have a museum built. There are also cars and engines outside waiting to be restored. It’s a great place to visit.