The Sages declared that if one leaves Eretz Yisrael for the Diaspora and plans to remain abroad, he is considered a resident of the Diaspora from the moment he arrives at a Jewish community there. From that point on, he is obligated to keep two days of Yom Tov (Pesaḥim 51a; SA 496:3).
However, if he intends to return to Eretz Yisrael, then he retains his status as a resident of Eretz Yisrael. Therefore, if he is not staying in a Jewish community (meaning he is spending Yom Tov outside the community’s teḥum Shabbat), he does not have to observe a second day of Yom Tov, and he may do melakha (SA 496:3).
However, if the resident of Israel is staying in a Jewish community (or within its teḥum Shabbat), he must behave as they do and make sure he is not visibly deviating from their practice (Pesaḥim 50a; SA 496:3). Therefore, he is not allowed to perform melakha on Yom Tov Sheni. True, some maintain that he may do so in private (Avkat Rokhel §26; Yam Shel Shlomo). However, according to most poskim, he must refrain from melakha even in private, because if he does not refrain, word is likely to get out, and this would undermine and detract from the community’s Yom Tov (Tosafot; Ha-ma’or; MB 496:9).
In accordance with his status as a resident of Eretz Yisrael, he should make havdala privately after the first day of Yom Tov and put on tefilin privately the next morning. To avoid being disrespectful toward his host community, he should make sure to honor Yom Tov Sheni by wearing Yom Tov clothes and lighting Yom Tov candles (without reciting a berakha). In terms of praying, it would seem simplest for him to pray alone at home, as the prayers he will be reciting will differ from those of the local congregation. They will be reciting Yom Tov prayers, while he will be reciting either Ḥol Ha-mo’ed prayers or weekday prayers (Oraḥ Mishpat §129). If he can attend part of the prayer service without its being obvious that he is not reciting the same prayers, this is preferable, as it allows him to hear Kaddish and Kedusha. If possible, it is also preferable that he recite the Amida with the congregation, while obscuring the fact that he is reciting a different Amida text.
If a resident of Israel is staying in his own apartment, he does not have to participate in a second Seder. If he is a guest of Diaspora residents, though, he should participate in their Seder but not recite the berakhot over the various mitzvot of the evening. Rather, he should simply respond “Amen” to his hosts’ berakhot (Ḥayei Adam 103:4).
As I wrote above, the obligation to follow the practices of the Diaspora pertains when one is within the teḥum Shabbat of a Jewish community. This is the approach of the poskim cited by MB 496:10. It can be inferred that they are not worried about the presence of individual Jews. It also seems that these poskim do not take into account the presence of non-observant Jews, even if there are more than ten of them, unless they are part of an organized Jewish community.
. Rav Kook writes in Oraḥ Mishpat §129 that it is preferable that one not go to the synagogue if there is a possibility that he will be given an aliya. According to R. Shlomo Zalman Auerbach, even if he can hide the fact that he is praying differently, he is not obligated to go and sit through a long holiday service. It would seem that all would agree with this. The question is: le-khatḥila is it better for him to go? Of course, if it will be difficult for him to pray differently without its being noticed, then it is preferable that he not attend. However, if he can manage to obscure the difference, many write that it is preferable that he attend in order to pray with a minyan and respond to Kaddish and Kedusha (see Or Le-Tziyon 3:21:1; Si’aḥ Naḥum §28; Yom Tov Sheni Ke-hilkhato 3:17). R. Moshe Feinstein writes that if there is a particular minyan that one always attends, and his absence would be conspicuous, he should attend the minyan and discreetly pray the weekday prayers (Igrot Moshe, OḤ 3:92). He should attempt to avoid being called up to the Torah, but if they do call him up, he may go. If a Kohen attends the synagogue on what is for him the day after Yom Tov, and the congregation is praying Musaf, Maharam ibn Ḥabib says he should ascend to the bima and recite Birkat Kohanim, since it is permissible to recite the berakha multiple times on a given day. In contrast, Ginat Veradim (OḤ 1:13) argues that he should not ascend, since he is not praying Musaf. Rav Kook writes that the Kohen should ascend with the other Kohanim, but say the name of God inaudibly (Oraḥ Mishpat §129). If he is the only Kohen present in the synagogue, he may ascend and recite the berakha (Or Le-Tziyon 3:23:2).
Ten male residents of Eretz Yisrael may not convene a weekday minyan on Yom Tov Sheni in the Diaspora, even in a private home. Even though Jews from abroad who visit Israel generally do form minyanim for the second day (as explained below in section 9), this is because the rabbis in Israel have allowed it; in contrast, this is not the customary practice abroad. This is the approach of Har Tzvi 2:78; Or Le-Tziyon 3:23:1; R. Shlomo Zalman Auerbach and R. Shalom Yosef Elyashiv (cited in Yom Tov Sheni Ke-hilkhato ch. 3 n. 76). I have heard that there are places in the Diaspora where Israelis do have a minyan with the permission of the local rabbis, relying on the custom of Diaspora Jews visiting Israel.
. Some maintain that even if he does not have a separate room, if he can avoid sitting with them he should (R. Shlomo Zalman Auerbach and R. Shalom Yosef Elyashiv, as cited in Yom Tov Sheni Ke-hilkhato ch. 3, n. 84). Or Le-Tziyon 3:23:1 states that according to Sephardic practice, one should not participate in a second Seder. This is left as a matter of choice.
Since the accepted ruling is that one should not do melakha even privately, of course he may not eat ḥametz on the eighth day of Pesaḥ, which is Yom Tov Sheni in the Diaspora (AHS 496:5).