This is the discussion referred to in the footnote:
*** w90 2/15 p. 14 pars. 21-22 From Seder to Salvation ***
The Hebrew day ran from sunset (about six o’clock) to the next sunset. God commanded that the Passover lamb be killed on Nisan 14 “between the two evenings.” (Exodus 12:6) When would that be? Modern Jews cling to the rabbinical view that the lamb was to be slaughtered near the end of Nisan 14, between the time when the sun began to descend (about three o’clock) and the actual sunset. As a result, they hold their Seder after sundown, when Nisan 15 has begun.—Mark 1:32.
We have good reason, however, to understand the expression differently. Deuteronomy 16:6 clearly told the Israelites to “slaughter the passover sacrifice, in the evening, at sundown.” (Jewish Tanakh version) This indicates that “between the two evenings” referred to the twilight period, from sunset (which begins Nisan 14) to actual darkness. The ancient Karaite Jews understood it this way, as do Samaritans down to today. Our accepting that the Passover lamb was sacrificed and eaten “at its appointed time” on Nisan 14, not on Nisan 15, is one reason why our Memorial date sometimes differs from the Jewish date.—Numbers 9:2-5.
This was a matter of some rabbinical debate and controversy in later Judaism as it involves some rather technical terms, but the position the Society takes is clearly the more problematic one. First of all, the redacted narrative in Exodus 12 presents Yahweh as striking down the firstborn sons in Egypt "on the same night" that the Israelites eat the Passover meal (v. 12), specifically "at midnight" (v. 29), and it was "during the night" when the Egyptians discovered that their children had been struck down and mourned them (v. 30), and it was also "during the night" when Pharaoh told Moses and Aaron to take the Israelites and "hurry and leave the country" (v. 31-33), and so the Israelites promptly left Raameses (v. 37). The Israelites left so quickly they did not have time to prepare the bread (v. 39), for they "left Egypt in haste" (cf. Deuteronomy 16:3). There is no indication that they waited a whole day until the following night. But in Numbers 33:3 we read that "they departed Ramesses in the first month on the fifteenth day of the first month, on the morrow after Passover". If the Passover meal was held early on Nisan 14 (as the Society holds), then the Israelites would not have left right away (as it would have still been Nisan 14). As the Society itself states, if the Passover lambs were slaughtered prior to sunset, "the Passover meal itself would have been eaten in Egypt on Nisan 15 and the Israelites would not have left Egypt until that date" (Watchtower, 15 March 1973, p. 175). Yet that is in fact the date given in Numbers 33:3.
Second, the meanings of "in the evening" (ba`ereb) and "at sundown" (bô' haššamesh) in Deuteronomy 16:6 are not necessarily what the Society assumes. With a day reckoned either from sunset to sunset or as a period of sunlight in contrast to night (as in Genesis 1), the "evening" was often presented as the close of the day (yôm). It is the time when the day's work ends (Genesis 30:16, Judges 19:16, Ruth 2:17, Psalm 104:23), when one may draw water for the night (Genesis 24:11), or set up camp for the night (2 Samuel 11:13, Zephaniah 2:7). Since work is forbidden on the Sabbath, the "evening" here would have to mark the end of the day. Sundown could either refer to the descent of the sun towards the horizon during the afternoon or the descent of the sun across the horizon itself (equivalent to what we refer to as "sunset"). But let's assume for the sake of argument that it refers to sunset. Would the slaughtering of the paschal lamb at sunset occur at the end of the day or at the start of a new day? The Society interprets the phrase as necessarily the latter. But this is not consistent with its usage elsewhere. So for example, we read in Deuteronomy 21:23 that one "must not leave the body hanging on a tree overnight; be sure to bury it that same day, because anyone who is hung on a pole is under God’s curse". The removal of bodies from trees at sundown in Joshua 8:29 and 10:27 reflects this provision in D (as does John 19:31). But in both passages we read that Joshua gave the command to remove the corpses "at sundown" (bô' haššamesh) and in 8:29 we further read that the corpses remained on the trees "until evening" (`ad `eth-`ereb). Since the action reflects the law commanding the removal of the bodies "on the same day", the phrase "at sundown" points to a time at the end of the day. In parallel to this, the paschal lambs in Deuteronomy 16:6 would be slaughtered towards the end of Nisan 14, not at the start of the day.
The most difficult phrase is "between the evenings" (bên ha`arbayim) in Exodus 12:6, a wording that sounds particularly obscure in English (and it may also have been an idiom in Hebrew without this literal meaning). But here again usage points rather clearly to a time in the late afternoon at the end of the day. With regard to the Tamid sacrifice, we read in Numbers 28:3-4 that two lambs are to be sacrificed each day, "one lamb in the morning and the other between the evenings (bên ha`arbayim)". In Daniel 8:14, 26, the time of the latter sacrifice is simply "evening" (`ereb). Notice that in Numbers 28, the morning sacrifice is mentioned first followed by the one "between the evenings", and both occur in a single "day" (yôm). Unless the second lamb is killed before sunset, it could not be killed on the same day as the first. Josephus understood the text in the same way, he wrote that the law requires "a one-year-old lamb be killed every day at the beginning and at the ending of the day" (Antiquitates, 3.237). Here he uses the Greek word hemeras "day" in its usual sense as the period of daylight from sunrise to sunset (as opposed to nux "night" as the period from sunset to sunrise). The morning sacrifice occurs at the "beginning of the day" and the evening sacrifice occurs "at the ending of the day".
Such an understanding can be found in the LXX translation of the Pentateuch (mid-third century BC); the phrase "between the evenings" (bên ha`arbayim) is rendered "in the afternoon" (to deilinon) in Exodus 29:39-41 LXX. The earliest explicit commentary on the timing of Passover can be found in Jubilees (second century BC). There we read that "the children of Israel will be the ones who come and observe Passover on its appointed day on the fourteenth of the first month between the evenings from the third part of the day until the third part of the night because two parts of the day are given for light and one third for evening" and "they shall sacrifice the Passover at evening when the sun is setting on the third part of the day" (49:10, 19). This utilizes an Essene division of the day into three segments (6am-10am, 10am-2pm, 2pm-6pm), the third of which is set aside for "evening", and the night similarly divides into three parts (6pm-10pm, 10pm-2am, 2am-6am). This passage clearly states that the Passover begins "from the third part of the day", with the sacrifice occurring "at evening when the sun is setting on the third part of the day". This puts the sacrifice towards the end of the day between 2pm and 6pm, probably close to sunset "at evening" when the work for the day is done. Passover is thus observed from then until 2am on Nisan 15. Then in the first century AD, we have another explicit statement by Josephus. He wrote that the high priests, "upon the coming of their feast which is called Passover, slay their sacrifices from the ninth hour till the eleventh" (Bellum Judaicum, 6.423). The "ninth hour" begins at 3pm (cf. Matthew 27:45, Mark 15:33-34, Luke 23:44) and the "eleventh hour" begins at 5pm. This shows that when Passover was observed at the Temple in the first century AD, the paschal lambs were indeed slaughtered at the end of Nisan 14, between 3pm and 5pm, and not early on Nisan 14 just after sundown.