Donald J. Trump’s campaign has signaled strongly to Republicans in Washington that he will pick Mike Pence, the governor of Indiana, as his running mate, though Republicans caution the party’s mercurial presidential candidate may still backtrack on his apparent choice. Trump’s advisers have told national Republican officials that they are preparing to make an announcement with Pence, according to three people with knowledge of the conversations, who were not authorized to discuss them publicly. His campaign said that it will unveil a running mate for Trump in New York on Friday. On Wednesday, Trump and his children threw together a hasty series of conversations with other finalists in the vice-presidential search, including Gov. Chris Christie of New Jersey, Senator Jeff Sessions of Alabama and Newt Gingrich, the former House speaker.