There are a number of indications pointing at an origin from an ancient dance.
To answer your original question, the meaning of toit I would select out of all those cited by wiktionary, is... surprise surprise... the French one.
A toit is the French word for "roof" and I've got this "folk etymology" to propose. It's absolutely unverified and even denied by proponents of the theory that rhyme reduplications are mostly driven by rhymes rather than by meaning.
However the excerpt it quotes is from 1680 and I don't rule out the explanation proposed by the prolific A.A. (in Notes and Queries, a scholarly journal).
Here is a scan from this particular excerpt.
I took it from the www.archive.org Internet Archive at this particular URL.
The other reduplication mentioned in this excerpt (tolly-polly) is known to be an ancient dance.
For those interested in exploiting this interesting albeit unproven gold mine of antiquities, the first document to get hold of is the ebook "A Bibliography of English Etymology". The index entry cites both the author of the note and the source. In our case you will find the following entry
A.A. 1865d; L. 1853d: 391; Saintsbury, George. 1928: 64
So you need to look for a note signed by "A.A." in the reference 1865d, another note signed "L." in the reference 1853d and a note by George Saintsbury in the reference 1928.
These references lead respectively to volumes 7 and 8 of Notes and Queries.
Here is the second excerpt. Not that this second explanation also refers to a dance.
I could not find the 3rd reference. It points at a book by "George Saintsbury" titled "More words!" (a sequel to his first issue "Words! Words! Words!" published in 1927).
I've just had a look at the OED and the oldest quote there is from around the same period and also hints at an ancient dance:
1668 R. L'Estrange Vis. Quev. (1708) 100 The Widows I observ'd‥ Chanting and Jigging to every Tune they heard, and all upon the Hoyty-Toyty, like mad Wenches of Fifteen.
The Irish/English jig being, in turn, the origin of the French dance named "gigue".