To run at great speed away from something.
To flea or to immediately vacate an area in the opposite direction without regard to barrier or obstacle and in all cases continue to vacate until perhaps lost, and most definitely until one is out of all possible sight and vicinity of the area or activity that one is trying to vacate from, releasing excrement while in the process of hightail ('hightailing', or 'hightailing it').
The cause for ceasing the activity of hightail ('hightailing' or 'hightailing it') is physical exhaustion.
The example is from the activity that the term applies. This is referring to deer, (antelope, caribou, et. al.).
Example #1: "When I fired rifle at the large buck and missed the buck hightailed it."
(When this animal is frightened it will turn raise its tail, drop all possible excess weight (release excrement) and run in the opposite direction until exhausted.)
Example #2: When I came out of the Butthole Surfer's show in Smyrna Florida and I saw a parking lot full of skinheads with chains and pistols, cowboy-rednecks with ax handles and shotguns and cops with batons and teargas, Marc and Tyler my little purple haired California punk-rock-ass, hightailed it all the way back to Orlando.
Once I saw the cops, I hightailed it out of there.