Tosefta zu Divrej Hajamim II 30:18

A convert who converted between the two Passovers needs to observe Pesach Sheni, the words of Rebbi. Rabbi Natan says, there is no need [for him] to observe Pesach Sheni, since he was never obligated in Pesach Rishon --[just as the obligation] of building the Chosen House was placed upon Israel (i.e., just as non-Jews are not obligated to build the Temple, and their conversion does not impose an obligation to build a Temple once it had already been built, so too does their conversion not trigger an obligation to observe Passover once Pesach Rishon has passed). The individual [is obligated] to observe Pesach Sheni, but the community [is not obligated] to observe Pesach Sheni. Rabbi Yehuda says, even the community [is obligated] to observe Pesach Sheni. Said Rabbi Yehuda, it so happened with King Hezekiah that he had the [whole] community [of Israelites] perform Pesach Sheni, as it is said (2 Chron. 30:18), "For most of the people -- many from Efraim and from Menasheh and from Issachar and from Zebulun -- had not purified themselves [but they ate the Passover offering in violation of what is written]." Rabbi Shimon says, it wasn't because he had the community perform Pesach Sheni, but rather because he intercalculated [the month of] Nissan during Nissan, despite the fact that only [the month of] Adar may be intercalculated [during a leap year]. Rabbi Shimon bar Rabbi Yehuda says in the name of Rabbi Shimon, and it was also that he had the community perform Pesach Sheni (i.e., he acted improperly both in this way and in intercalculating the month of Nissan during Nissan). § They may not form a group [of registrants comprised] of women or of slaves or of minors, so as not to drag out the prayer service (see Tos. Pesachim 4:9).