In Deathnote, when L received a recording from the T.V. channel which he concluded to be second Kira, he replied to it disguising as Kira.
However, during the subsequent conversation, only the second Kira and L's team acting as Kira conversed. In other words, the real Kira (if Light was not Kira) didn't reply at all. Don't you think this would be even more of a proof that Light is Kira.
Therefore, why Light didn't reply to second Kira's recordings separately? This not only would have given him a chance to talk to second Kira but also to demand something from her.