Here's a link to the post about this rhyme/cheer that I just published on my blog

http://pancocojams.blogspot.com/2011/12/childrens-rhyme-gigalo-examples.html The Children's Rhyme "Gigalo" - Examples & Probable Sources

That post includes text examples, commentary, and videos of the American rhyme/cheer "Gigalo" (Jigalow) and the British rhyme "(My Name is) High Low Jackalow.

I believe that the line/rhyme title "My name is high low jackalo" and similar names such as "high low peccalo" that are found in the British children's rhyme and the word/title "gigalo" ("jigalo") are all folk etymology forms of the title of the card game "high low Jack". That card game was very popular in the 19th century and is apparently still popular now. Other names for the "High Low Jack" card game are "Pitch", "All Fours", and "Old Sledge".