The term “Touch wood,” which became “Knock on wood” in America, is derived from a Scottish and English game of Tag called “Tiggy Touchwood.” In Scotland, “It” in a game of Tag is “the Tigger” or “Ticky.” In the UK, “It” is “Tiggy” or “Tig.”
The Tigger starts the game by saying:
Tiggy, tiggy, touch wood,
My black hen,
She lays eggs for gentlemen.
Sometimes nine and sometimes ten,
Tiggy, tiggy, touch wood,
My black hen.
Everybody scatters, and they try to go somewhere with wood, so that they can touch it and be safe. Different areas have different definitions of “wood,” but trees and sticks usually do not count. (There’s also a variant called “Touch Iron,” and presumably other substances could also be used as safe bases for Tag.)
Of course, part of the fun is not staying at a safe base, and in many variants it must be announced that someone is arriving at or leaving a safe base. There are also variants where there is a time limit on being able to touch wood and be safe.
I thought it was interesting to learn about Tiggy Touchwood, especially since it never occurred to me that Tigger was always playing Tag.
Aliens in This World 
Interesting. I learned it as “Hickety pickety, my black hen…” (all the rest the same, except “Hickety pickety” used again at the end. Of course we all know about “Knock on wood,” which seems related.
Almost certainly the other way around in my opinion, given that animistic beliefs etc. have had people around the world viewing trees as homes to spirits for centuries if not millennia