Thank you for the useful information, Edokko101-san. It was very helpful, and ed me to the following:
I finally figured out that visitors must be guided, in a group only, by a person dressed in a rabbit costume, who gives short talks. Musical presentations are made by other people dressed in rabbit costumes. Nobody is allowed all the way down into the station, the doors down to the platform are locked, and the platform is not even visible. Thus, you can still only see the platforms of the old station while riding the train from Ueno to Nippori, assuming they have any lights on. I've seen that a few times already, but have always wanted to be able to stand on the platform.
While I am disappointed with this restriction, there was a very short video of the portions of the station that are shown on the tour. Having seen the video, there is no need to go in person.
There is lots more background information about the rabbits and their association to the station, and a large rabbit statue in the station's main entrance. Yes, I know the history & details, and no I won't go into them.
I was surprised to learn that there is another entrance to the station, between the park and the Art Gallery (not the Art Museum). You can just barely see it on Google street view, since street view doesn't go into parking lots. You can't see it from the satellite view, as it is covered with trees. I didn't see in the photos or video where it connects, underground, to the station.
There might have even been another station between the Hakubutsukan station and the tunnel entrance. It is where the 7-11 is now. The translation software called it Kaneiji Station. Kaneiji temple is close by (various translation software also call it Kannaji and Kannoji).
This is a convoluted link, so after it finishes doing whatever, click on the black x at the upper right to get back to the main article.https://www.facebook.com/uenoyes/photos/a.2208615809371397/22529383549...
As for getting the tickets, there will be someone in the park holding a big balloon. I assume the tickets will be available in that general area.
Thank you again for your kind assistance.