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.
Back means the opposite of front: back window. Hind, and the more formal word posterior, suggest the rearmost of two or more often similar objects: hind legs; posterior lobe. Rear is used of buildings, conveyances, etc., and in military language it is the opposite of fore: rear end of a truck; rear echelon.