You, like most Americans, probably plan to run for president. You have plenty of time, theoretically; the general election is still 22 months away and even if you plan to seek the nomination of one of the major parties, those don't kick off until January.
Rearing is a common measure of activity and exploratory behavior used in the open field and sometimes in certain mazes. Nothing else. But I agree it could be related to very specific behaviors. I like the idea of escape.
So lumbering in the wake of his thoughts means that Uncle Vernon's thoughts are following in the same line (in the wake of) of Harry's thoughts, but doing so behind him (in time, in realization, in conclusions), slowly and awkwardly (in a lumbering manner). The meaning of following sounds more suitable now.