To understand skilligimink, one must read the original sources. Here’s a prime example from the book Lulu, Alice and Jimmie Wibblewobble by Howard Roger Garis, chapter XI – Alice Wibblewobble’s Enchanted Castle.

Alice Wibblewobble goes on a walk and sees an amazing sight.

Then they went on a little farther, and, in a short time . . . they came to a most beautiful place. I wish you could have seen it! At first Alice thought the rainbow had fallen from the sky, there were so many colors. There was red and green and blue and orange and violet and yellow and pink and purple and even some of that skilligimink color, that once turned Sammie Littletail sky-blue-pink.

Then the little duck girl saw that the colors were all from different flowers that smelled just like mamma’s perfume bottles.

From Project Gutenberg‘s Lulu, Alice and Jimmie Wibblewobble by Howard Roger Garis. (emphasis added)