LOL. It's a mento. Mento, if you're unsure, is a Jamaican "folk song" style similar to calypso. It's based in tunes for the old, indigenized version of the quadrille. The tunes, as songs, easily cross with group-play game-songs. Most Jamaicans probably know the tune (but not necessarily where it came from) as well as you'd know any nursery rhyme—it's just a piece of culture.

For example, you can hear Lovindeer riffing on the tune here, at 0:58:
https://youtu.be/_1aS7IPlAC4?si=_mlaQhlIwWUAqkPe

Here's another ragga track that steals it for the chorus:
https://youtu.be/AzAACzeYzrw?si=N_Mnq1clA4Y2fEtC

I don't even know where all I've heard it—it's just "there," in the culture. Also, Jamaicans love the phrase "Mi no want"—it's a really catchy hook that you can follow with whatever.

From the sound of it, I strongly suspect that it's "traditional" from the 19th c. folk song repertoire, however I can't cite any source for that. It just sounds exactly like all the songs from then: the rhythm, the tune, the patois lyrics about rural stuff and sex.

There's always the possibility that some popular recording re-distributed it. So...

It was recorded among the earliest recordings of the Jamaican music industry, by The Jamaican Calypsonians, under the title "Miss Goosie":
https://youtu.be/pzsTuRTNrHM?si=DkH4uyxn9_Ls4DEq

This earliest recorded music was a dressed-up version of mento. Kind of an urban arrangement of the rough, rural mento music which was strategically marketed under the label of "calypso."

This performance is a medley, I think having three songs. Ends with "Drive Her Home." What I'm calling the first *two* songs have been linked by the "Goosey" theme. That is, the first song is about Mr. Goosey in the bed of his mistress, and the second song--I believe it is a second song and not a continuation of the first--is the song in question, best labeled as "Gungo Walk." But the performer has slipped in the name "Goosey" into Gungo Walk to connect them.

The lyrics to this rendition of "Gungo Walk" are like:

Mi no wan', mi no wan' weh [Goosey] wall a left
Mi no wan', mi no wan' weh [Goosey] wall a left
Goosey run a mile and a half inna gungo walk
Goosey run a mile and a half inna gungo walk

As for the first song, you can hear a later, reggae adaptation of this bawdy song—without the Gungo Walk part—here, by Max Romeo (who began his career as a bawdy reggae singer):
https://youtu.be/BOXfOXaxClg?si=5WvRmPwavsxlnioE

Max Romeo does reference the "gungo walk" imagery though, so maybe these "two" songs are connected after all.

Incidentally, whereas many narrators of the history of Jamaican music WRONGLY assert that the mento was a building block of the ska that kicked off Jamaican's popular music in earnest in the early 60s, countryside-based mento wasn't much of an influence at all. It wasn't until around 1968, with the advent of "reggae," that musicians reached back to mento as an influence. Mento sort of disappears again in the 70s as reggae strays from its bawdy roots into this "righteous" thing, but then after Bob Marley dies and the dancehall DJs bring back the old school bawdry in 1981, it's back again.

A Trinidad-style calypsonian, Lord Kitchener, did a rewrite, "Old Lady Walk a Mile and a Half," which is almost unrecognizable. The melodic rhythm, though still very syncopated, has been somehow "flattened out" as I hear it -- it's taken away the core "mento" rhythmic feeling.
https://youtu.be/lpSHoteeGic?si=pvmHA4YPnCbiiG4i

Clint Eastwood and General Saint are DJs (MCs in USA hip-hop parlance) toasting in rub-a-dub dancehall style over the "Taxi" riddim. They are just riffing on fragments of Jamaican musical culture. After all, re-mix and hip-hop derive from this Jamaican aesthetic. Hence, when they riff on the Gungo Walk melody, its another parody (but not as extreme as Lovindeer's!):

Mi no wan', mi no wan' weh di man dem wall a left
Mi no wan', mi no wan' weh di man dem wall a left
'ca man Goose run a mile and a half inna matey gungo walk
'ca man Goose run a mile and a half inna matey gungo walk

"Matey" is mistress.
"Gungo walk" is the space between rows in a field of gungo peas (pigeon peas). You can think of walking between the gungo peas as a rough metaphor for intimacy in the sense of romantic involvement generally, or more specifically as a metaphor for a penetrating a vagina.