Sweet Honey's version of the Little Red Caboose is another one of those spiritual-type train songs (on the theme of everyone get on board). They list it as their arrangement of a traditional song. I'll bet the kids' song is just a fragment of the original.

(I first heard it on a great compilation of songs for kids that was given at my son's baby shower (thanks, Don and Loti!), "A Child's Celebration of Song", from Music for Little People, distr. by Warner Bros.)

The chorus is (2x) Little red caboose, little red caboose
riding behind that train

~ Becky in Tucson, AZ

But the verses are:

Get your ticket and get on board
riding behind the train
Get your ticket and get on board
riding behind the train

I've got a brother on that train
riding behind the train
You've got a sister on that train
riding behind the train

Ppresumably you could go through all the assorted relative in the usual fashion.