I think this panel holds the key to beating it if you notice how the sound waves move. I think Souichi is detecting that the handkerchief is on the ground, not that Baku is in the process of dropping it. He always clicks to check that its there before turning around; Baku is just dropping it so quickly that he is always clicking when it's there - meaning we haven't seen him click when it's not there, and not turn around yet.
Do we know that Baku specifically has to stand behind Souichi and drop the handkerchief like they have been doing? Considering that he was able to move in front of Souichi during his turn makes me think they have some freedom, and that Yakou just needs to see the handkerchief hit the floor. Could he obscure that somehow with his body, or an object? Like turn around and drop it facing away from the chair?