Having been away for the weekend, I didn't start this puzzle until last night, and sailed steadily through to the CLOSEBYAMPTHILL acrostic. But then I couldn't make sense of the very final step. After reading this forum, I'm a bit relieved that no-one else has an absolutely convincing solution either, though I like buster's idea of the drawing of a (rather abstract) hare by highlighting all the various forms of SEARCHAREA.
If I may be excused for "raising a hare", I wondered whether "four consecutive letters" could refer to "consecutive letters of the alphabet". I noted that, in the third row, the letters Q, R, S and T appear consecutively (though not contiguously), so they fit, in a rather forced way, the "four consecutive letters in a straight line" requirement. On this basis, the "search area" would be the whole grid. But this would be such an anti-climax that I can't believe it's correct.