Tokyo Disney Caboose *PIC*

Indeed, Tokyo Disneyland does own the ex-Magic Mountain caboose, aka #0409 (linked a picture below).
What's interesting is that Tokyo Disneyland's railroad is 30" gauge...the same gauge shared by Disneyland's former Viewliner and Mine Train, as well as the Fort Wilderness steam trains in Orlando. All other Magic Kingdom railroads have been 36", as usual.
The caboose is on static display; it isn't used. It's around with several other artifacts at a sort of dummy depot/MOW shed. I don't know how exactly it ended up in Tokyo...
What's interesting about that the Tokyo Disneyland Resort is owned and operated by the Oriental Land Company, not the Walt Disney Company! Disney designs the parks and attractions and collects royalties/licensing rights from an agreement dating back many years.
The four steam locomotives in-service there were built by Kyosan-Kogyo in Japan. The first three were roughly based on DLRR #4, which in itself was a rebuild of a 1925 Baldwin teakettle to resemble D&RG #1 "Montezuma". The steam dome and sand dome are reversed on the boiler on the Tokyo engines (really noticeable on the cap-stacker); with some Japanese design characteristics to be found in several places, including the abnormally-long cylinders.
-Ed Kelley