I agree that Twain will probably be a Republican, though by the 1890s he will be somewhat odd, since he will be an old Lincoln Republican, for civil rights and internal improvements, rather than Gilded Age corporate Old Guard. We might tweek his later carreer; say his later investments pan out and he's not broke in his later years. Rather than make a speaking tour for money, he does so for fun and for "the public enlightenment." This catches the attention of a party boss, who realizes that Twain will make a great US Senator, since he'll have popular support and at that time US Senators were appointed by their state legislatures. The idea fizzles, until some senator who lived OTL, died and Twain was appointed to the Senate.
The odd thing also is that Twain, who I imagine being a Progressive like TR, will indeed breath a rhetorical fervor into anti-imperialism debates about the Spanish American War. Though he and TR will be allies domestically, they will be opponents regarding international policy. When TR invites WEB DuBois to the White House, he also invites Senator Clemens to the same meeting. Clemens gives all sorts of speeches about civil rights. I think TR probably bows out in 1908 as he did OTL, but will come back in 1912. Here's the great part: since his life hasn't been so hard, Clemens does not die in 1910 (messes up the Halley's comet bit, but I think it's worth it). When TR makes a bid for the presidency against Taft, Clemens is with him and ends up as his running mate; the combined pair may win the nomination, but Clemens probably just enfuriates the Old Guard even further. Hence they still run as Third Party, but Clemens can take over the campaigning to great effect when TR is out from being shot (assuming he still is).
Presto chango: not only is Mark Twain in Politics, he ends up as Vice-President of the United States and a hero of an earlier Civil Rights Movement! He's probably too old to contest the Presidency in 1916, but TR may run again if WWI occurs on schedule.