At what point and why did Near start to suspect the presence of a second Death Note? How and why did he consider that Mikami used a faked one?
L already suspected that there's more than one Death Note, so Near knows that there are two notebooks. Fact one came into consideration at the time of the kidnapping of Kiyomi Takada, when Mikami went to the gym a second time. He behaved suspiciously, and took the actual Death Note and wrote Kiyomi Takada's name. It is revealed at the end of the Death Note.