×As stated in Cerebral Testing Facility 1N1E, between equal-length paths, brains prefer the orthogonal directions, then Wait, then diagonal directions.

Before forming the fluff blob, the roach can reach either (17,12) or (20,12) in five moves either by starting with Wait or with west/east; because of this, both moves lead to equal-length paths to Beethro no matter where he is in the room. And west/east will always be preferred over Wait.

With the fluff in place, when Beethro is on the west side of the room, it takes five moves to reach (17,12) starting with Wait and six starting with an east move. Once the roach is on the west, the brain's first choice will now be Wait -- and in that case, monsters (except golems/wubbas/gel babies) ignore the brain and make an unbrained move. (And the converse applies when Beethro is on the east side of the room.)