I have been trying to find biographical information about Eldad and Medad
but cannot seem to find a source which states which tribe they are from. The Baale Tosfot - Daat Zekeinim says they were related to Moshe but does not cite a source for this.
2 Answers
According to Bamidbar Rabba 15 19, Eldad was Alidad ben Kislon and Meidad was Kemuel ben Shaftan.
That would put Eldad as the Nasi of Binyamin and Meidad as the Nasi of Ephraim as found in Parshas Masei 34 vs 21 and 24.
The idea that they were related to Moshe is found in Targum Yonasan Bamidbar 11 26. There we see that when Amram divorced Yocheved she had these two sons from Elitzaphan ben Parnech. In Bamidbar 34 25 we find him listed as the Nasi of Zevulin.
And then there is the Daas Zikeinim mentioned by the OP found in Bamidbar 11 27. There we find the idea that Amram fathered them after Har Sinai when he and Yocheved heard they couldn't be married since she was his aunt, and he went and married a different women.
That would of course put them in the tribe of Levi.
(Interestingly, a source mentioned in the D.Z. calls them paternal half brothers of Aharon, and doesn't mention Moshe.)
The D.Z. also quotes the idea previously mentioned from Bamidbar Rabba.
This link explains a lot and brings the sources from the answer above as well, but it also adds a footnote to Igrot Kodesh Vol 15 letter 5537, where the Lubavitcher Rebbe answers when Amram might have separated from Yocheved and fathered Eldad and Medad, according to the tradition brought by the Daas Zekainim. Basically, it seems like he answers that Amram may have become aware prophetically of the future issur of arrayos and separated from Yocheved again, at some point after Moshe was born (perhaps learning about it through Moshe.) https://www.chabad.org/parshah/article_cdo/aid/4407977/jewish/Eldad-Medad-The-Mysterious-Prophets.htm Igrot Hakodesh Vol. 15 linked here: https://www.hebrewbooks.org/pdfpager.aspx?req=15912&st=&pgnum=236