The term 'be on the brink' can be described by the crossword solutions of TEETER (6 letters), EDGE (4 letters), NEAR (4 letters), TEETERED (8 letters), and VERGE (5 letters). TEETER means to move unsteadily from side to side, EDGE refers to the line where two surfaces meet, NEAR is a synonym for close, TEETERED means to move unsteadily as if about to fall, and VERGE is the brink or point of an action. Therefore, the phrase 'be on the brink' can be interpreted as being close to a certain action or event, and having the potential to move unsteadily in either direction.