As you can see in the catalogue of S57-6 (June 1982) the Carina featured in the Paris-Dakar rally. According to the Carina page on the Japanese Wikipedia it featured in 1981 and 1982. However I could not find any reference that they actually did attend in 1981, especially not on this list. I did find a Toyota Starlet attending Paris-Dakar.

I did find that Masaru Kubota and Masahiro Uchida joined Paris-Dakar in 1982 and 1983 with a Carina, and Kubota was driving the Starlet in 1981. They became 34th in 1982 but did not finish 1983.

They entered as a private team in the normal unmodified class, so their Carina was almost bone stock! Although they did not have any factory backup I doubt that Toyota did not actually supported them. Even worse: when they did finish Toyota used it in any way they could!
Perhaps the Japanese Wikipedia page is mistaken about the years, maybe the conversion from Japanese years was done wrongly or maybe they traveled to Paris before 1st of January and of course counted it as 1981. We'll never know.
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