Chabad.org — English translation + Rashi
Torah Temimah: “ככל חקת הפסח יעשו אותו” — the general rule is that the statutes of the first govern the second, except where the Torah explicitly distinguishes.
English: “According to all the statute of the Pesach they shall offer it” — a general clause that carries the core laws of the first to the second.
General transfer clause — the Torah itself states that the statute travels with the name.
Unless a specific exception is taught, the second Pesach is performed under the same statute as the first.