Our Gemara (according to our girsah not Rabbeinu Chananel s girsah) discusses the word Hazeh. Sometimes the Geamra exludes Pesach Doros and sometimes it only excludes Pesach Sheini. When it comes to the mitzvah of eating the Pesach on the night of the 15th, the Gemara says that Hazeh doesn t exclude other Korbonos that are in the month of Nissan.
This answer (following our girsah) only answers why we eat Pesach Rishon on the night of the 15th, since it is in the month of Nissan. It doesn t explain why we don t exclude the Pesach Sheinie. Perhaps Pesach Sheini can be eaten on the aft. of the 14th too.
How do we know that Pesach Sheinie is eaten only the night of the 15th of Iyar?
The Rambam in Hilchos Korbon Pesach Perek 8 Halacha 3 says And so too, the mitzvah of eating the meat of the Pesach Sheinei on the nights of the 15th of Chodesh Iyar is Mitzvas Aseh like it says by it, Al Matzohs U mrorim Yochluhu.
Where do you see from this Posuk that it is a mitzvah to eat the Pesach Sheini on the night of the 15th? Perhaps you may eat the Pesach Sheini with the Matzoh and Moror on the afternoon of the 14th too?
So that s 2 points:
1: Why would we have to eat the meat of the Pesach Sheinie on the night of the 15th?
2: How does the Rambam see it from the Posuk?
I suggest the following answer:
The Gemara on 95a discusses the klal of Mitzvohs Sheb goofoh.
The Gemara split up the mitzvohs that are included and excluded from Pesach Sheinie based on the 3 mitzvahs mentioned that the Torah mentions.
From Al Matzohs U mrorim Yochluhu, which is a positive Mitzvah, we learn out another positive mitzvah that the Pesach Shienie has to be eaten roasted. The Gemara doesn t add that the Pesach Sheini also has to be eaten the night of the 15th, which is also a positive mitzvah.
The Rambam however does bring the Posuk of Al Matzohs U mrorim Yochluhu as the source to eating the meat of the Korbon the night of the 15th, because we learn out the positive Mitzvohs that were included on the Pesach Sheinie from this Posuk.
And the Rambam goes out of the way to tell us that eating the night of the 15th, which was not discussed in the Gemara openly, is also learned out from the same Posuk.
Our Gemara also knew that once we include Pesach Rishon in the mitzvah to eat the Pesach at night, Pesach Shenie was also included. The Gemara must not have felt it even needed to be mentioned. The Gemara only excluded other dinim, like checking it for four days, which it seems is not Mitzvohs Sheb goofoh and Pesach Sheinie is excluded.
This answer is probably elementary, but since it s not discussed in the Gemara, and the Rambam does go out of the way to tell it to us, I thought that it should be brought up.
Tizku L mitzvohs
Yasher Koach! A similar explanation (using the foundation of Mitzvos shebi'Gufo, albeit with different Pesukim) is found in Teshuvos Binyan Tziyon (#30).
Kol Tuv,
Yaakov Montrose
Tizku le'Mitzvos
You raise a very important point. The Maharsha says that we know that Pesach Sheini must be at night from the fact that the Torah says that what is left over until the morning must be burned. However the Rashash objects that this does not preclude the possibility that the Karban may be eaten in the day. The Rashash answers that where we have another option we do not wish to make Pesach Sheini different from Pesach Rishon since the Torah stipulates "k'Chal Chukas ha'Pesach Ya'asu Oso". This is of course the basis for your answer as well, as this is the source for the learning out Pesach Sheini from Rishon on Daf 95a which you quote.
As for the Rambam it could be that he does not mean to say that we learn from this Possuk that the Pesach Sheini must be eaten only at night, rather that it is a Mitzvah to eat the Pesach Sheini as we see in this Possuk and that the time for this Mitzvah is at night.
However, after hearing your Pshat we do not need to say this anymore.
Thank you for your Pshat,
Dov Freedman