In principle, the kohanim should perform Birkat Kohanim any time the ḥazan repeats the Amida. Indeed, in Eretz Yisrael, the kohanim perform Birkat Kohanim at every Shaḥarit and Musaf. However, the Sages ordained that Birkat Kohanim should not be performed at Minḥa because it generally follows the afternoon meal, and there is concern that the kohanim will drink wine with the meal and then perform Birkat Kohanim under its influence, thus violating a severe prohibition. However, on fast days when Ne’ila is recited (such as Yom Kippur or fasts declared due to drought), since there is no concern that the kohanim will drink, Birkat Kohanim is performed at Ne’ila (SA OḤ 129:1; Peninei Halakha: Zemanim 7:12 n. 16).
Some say that Birkat Kohanim should be recited at Minḥa on Yom Kippur as well; since everyone is fasting, there is no concern about drunkenness. Moreover, on Yom Kippur, the time for Minḥa is late in the afternoon, just before Ne’ila (Behag), whereas all year long, Minḥa may take place at any point between just after midday and shki’a. Nevertheless, most Rishonim maintain that Birkat Kohanim it is not performed at Minḥa. Since, unlike Ne’ila, it is not recited at shki’a, people may erroneously conclude that Birkat Kohanim may be performed at Minḥa on weekdays as well (R. Amram Gaon). In practice, Birkat Kohanim is not performed at Minḥa. However, if a kohen ascends to perform it, he is not sent back to his seat; rather, he performs the blessing (Rambam; SA 129:1-2, 622:4; 623:5).
Ne’ila should be timed so that Birkat Kohanim is performed before shki’a, as many are of the opinion that this mitzva is analogous to the Temple sacrifices, which may be offered by day only (MB 623:8). Since Birkat Kohanim is a Torah commandment, we abbreviate, if necessary, the liturgical poems and supplications to reach Birkat Kohanim before shki’a. Be-di’avad, Birkat Kohanim may be recited during twilight, since it is uncertain that night has begun.
. Bedi’avad it is permissible for Birkat Kohanim to be recited until tzeit. This is the ruling of R. Shneur Zalman of Liadi (SAH 623:8); SHT 623:10 inclines this way as well. Several uncertainties factor into this ruling: 1) According to Raavya, Yere’im, and Or Zaru’a, Birkat Kohanim may be performed at night; 2) it is uncertain whether twilight is part of the day; 3) according to Rabbeinu Tam, shki’a takes place a while after sunset, which is still definitely part of the day. This ruling is accepted by R. Shlomo Zalman Auerbach and R. Yosef Shalom Elyashiv (as cited in Piskei Teshuvot 623:13); Yeḥaveh Da’at 6:40; and Or Le-Tziyon 2:8:13. They further write that Birkat Kohanim may be performed until 13.5 minutes after sunset. See Peninei Halakha: Shabbat 3:1 n. 1 and Harḥavot 3:1:14, where we explain that this period is at least 14 minutes in Jerusalem and c. 19 minutes at sea level in Tel Aviv.
Some maintain that a kohen who is not fasting should not perform Birkat Kohanim, even if he is the only kohen present (Kaf Ha-ḥayim 129:5; Torat Ha-mo’adim 3:4). Others disagree and say that this kohen should still perform it (Lu’aḥ Eretz Yisrael; Halikhot Shlomo, Tefila 10:13).