That was more of an anti-Taft, pro-Wilson move than anything else. Most of his campaign money for that came from Democrats.
There were two businessmen who financed TR in 1912, but I can’t recall their names. The American people easily fell for Woodrow Wilson, who was also a favorite of Richard Nixon. Barry Goldwater liked HST. We never find a Republican who admires an earlier Republican president it seems though some give lip service to Reagan, who was not nearly as conservative in action as his defenders claim.