Place it right after the wrong answer is revealed, as the closing beat of the fail. Follow it with the Windows XP Error Sound for a second layer of rejection, or open with the Law & Order Dun Dun to set up the reveal before the answer lands. Keep the buzzer as the final verdict, not the setup.
About this sound
This is the brief wrong-answer buzzer from Family Fortunes, lasting just over a second, with a bright electronic tone that cuts in and stops abruptly. It feels instantly damning and funny, like a public mark against a bad guess. The sound comes from the long-running British television game show, where it marked answers that missed the board.