As W. Labov has passed away, I came across a comment reposting this screenshotted request, along with the paper in question:
https://betsysneller.github.io/pdfs/Labov1966-Rabbit.pdf
The paper is quite a rollercoaster, ranging from describing of disturbingly racist ideas about native Hawaiian and Black children that some scientists still pushed at the time (1970!*), to Labov's own disarmingly cute and humane solution to the issue of testing children's language abilities.
Edit: *1970 - according to the article itself, which is apparently based on Labov's 1970 talk; however, the URL suggests that the article was published in 1966, which is contradictory. I'll try to find out where and when this was actually published...
Edit 2: It looks like it is from 1970, from Working Papers in Communication, vol. 1 (Honolulu: Pacific Speech Association). It is surprising that a recently published book also claims that it's from 1966, probably the authors got the file from the same URL with the wrong year.
Edit 3: The original Twitter thread: https://xcancel.com/betsysneller/status/1516848959284678656
As I'm reading this I'm getting angry. Not because of Labov himself (he's simply denouncing this crap), but because this sort of adult that he's describing is the one that I'd expect screaming with children.
And I'm glad that nowadays this sort of researcher would be barred from doing field work.
The rabbit approach was genius. Just like hiding himself behind the cloth hangers in another study; sure, nowadays this raises ethical concerns, but in his times it was the way to register spontaneous speech.