In the Mishneh Torah, Laws of Kings 11:1 (or 11:2 in some editions), Rambam brings verses to prove that the Torah "testifies to [the Messiah]", namely Deuteronomy 30:3-5:
וְשָׁב יְהוָה אֱלֹהֶיךָ אֶת-שְׁבוּתְךָ וְרִחֲמֶךָ וְשָׁב וְקִבֶּצְךָ מִכָּל-הָעַמִּים אֲשֶׁר הֱפִיצְךָ יְהוָה אֱלֹהֶיךָ שָׁמָּה: אִם-יִהְיֶה נִדַּחֲךָ בִּקְצֵה הַשָּׁמָיִם מִשָּׁם יְקַבֶּצְךָ יְהוָה אֱלֹהֶיךָ וּמִשָּׁם יִקָּחֶךָ: וֶהֱבִיאֲךָ יְהוָה אֱלֹהֶיךָ אֶל-הָאָרֶץ אֲשֶׁר-יָרְשׁוּ אֲבֹתֶיךָ וִירִשְׁתָּהּ וְהֵיטִבְךָ וְהִרְבְּךָ מֵאֲבֹתֶיךָ:
that then the LORD thy God will turn thy captivity, and have compassion upon thee, and will return and gather thee from all the peoples, whither the LORD thy God hath scattered thee. If any of thine that are dispersed be in the uttermost parts of heaven, from thence will the LORD thy God gather thee, and from thence will He fetch thee. And the LORD thy God will bring thee into the land which thy fathers possessed, and thou shalt possess it; and He will do thee good, and multiply thee above thy fathers.
To me, these verses speak about an eschatalogical "Messianic era", but not a Messiah per se. The classical commentaries "on the page" (ie. in my mikraot gedolot) agree, and not a one mentions the Messiah (excepting Ramban, but see there).
While it is possible to read that Rambam does not mean "testifies to [the Messiah]" but in fact "testifies to [the Messianic era]", this does not seem to be the simplest read. Indeed, the Chabad translation, for example, supplies "[Mashiach]".
In support of Rambam's idea that these verses testify to the Messiah as person, we have Targum Pseudo-Jonathan to Deut 30:4b (my translation):
... מתמן יכנוש יתכון מימרא די"י אלהכון על ידוי דאליהו כהנא רבא ומתמן יקרב יתכון על ידוי דמלכא משיחא.
... The Lord your God will gather you from there by means of Elijah the Kohen HaGadol (?) and bring you close by means of the King Messiah.
Question: Am I understanding Rambam correctly? If so, how does Rambam (and Targum Pseudo-Jonathan) read the verses to support this interpretation? Can this idea be found in other commentaries, or better yet, in the gemara or midrash?