One of the more frequent users (and most likely the originator as well) of the word Skilligimink is Howard R. Garis, the author of several books covering the adventures of Uncle Wiggily and his forest friends.
Here is a short chapter from his book “Uncle Wiggily in the Country” that shows one usage of the term. Click on to read the chapter, Uncle Wiggily and the Soup (pdf).
Please note that the reference takes place toward the end of the chapter. It may be interesting to also note that while Garis may be the originator of the word, it appears very likely that the tiddlewink is using it out of context in this chapter!