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The proof can be found here (pdf). It was published in 1838 and Gauss lived until 1855, so I would guess that he read it. Did Gauss say anything about it?

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  • $\begingroup$ Oswald Baumgart, Über das quadratische Reciprocitätsgesetz. Ph.D. dissertation, University of Göttingen 1885 (Dresden: B. G. Teubner 1885), 104 pp. makes no mention of such commentary by Gauss. Some of Gauss's correspondence with other scientists is available in book form, but only some of these books are accessible as Google scans. I have not found anything relevant yet in freely available scans. $\endgroup$
    – njuffa
    Mar 29 at 19:57
  • $\begingroup$ Baumgart's compendium of QR proofs is translated into English. As he remarks in final comments:"Probably Gauss did not publish the seventh and eighth proof because he intended to write a sequel to the Disquisitiones. And in fact the theory of cyclotomy, on which the seventh and eighth proof are based, was to be a part of this sequel. Thus it could happen that after about 60 years Lebesgue rediscovered the same proof already known to Gauss." Judging by "could happen", Gauss did not make any comments on Lebesgue's proof. $\endgroup$
    – Conifold
    Apr 1 at 6:13

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