To think that the Mosaic law did not promise eternal life implies that it did not provide eternal life, or salvation or justification. This insinuates that the old saints are not saved but went to hell.
The OT may not contain the NT term "eternal life" but whenever it promised "life" it meant exactly the same.
Daniel (12:1-2) 1 “At that time shall arise Michael, the great prince
who has charge of your people. And there shall be a time of trouble,
such as never has been since there was a nation till that time. But at
that time your people shall be delivered, everyone whose name shall be
found written in the book. 2 And many of those who sleep in the dust
of the earth shall awake, some to everlasting life, and some to shame
and everlasting contempt.
Deut (4: 1-2) “And now, O Israel, listen to the statutes and the rules
that I am teaching you, and do them, that you may live, and go in and
take possession of the land that the LORD, the God of your fathers, is
giving you. 2 You shall not add to the word that I command you, nor
take from it, that you may keep the commandments of the LORD your God
that I command you. ESV
Deut (10: 12-13) 12 “And now, Israel, what does the LORD your God
require of you, but to fear the LORD your God, to walk in all his
ways, to love him, to serve the LORD your God with all your heart and
with all your soul, 13 and to keep the commandments and statutes of
the LORD, which I am commanding you today for your good?
Lev 18:5 You shall therefore keep my statutes and my rules; if a person does them, he shall live by them: I am the LORD.
Deut 30:16 If you obey the commandments of the LORD your God that I
command you today, by loving the LORD your God, by walking in his
ways, and by keeping his commandments and his statutes and his rules,
then you shall live and multiply, and the LORD your God will bless you
in the land that you are entering to take possession of it.
All Jews believe that the law gives eternal life, even though some rabbinic Jews might not use the term.
Rashi commentary on Lev 18:5 -- You shall observe My statutes
and My ordinances: [This comes to include other details of [laws
pertaining to] this passage, that Scripture did not mention
explicitly. — [Torath Kohanim 18:142] Another explanation: [This
clause, ''You shall observe My statutes and My judgments, which a man
shall do,'' was added,] in order to apply ''observance'' (שְׁמִירָה)
and fulfillment (עֲשִׂיָּה) to statutes, and to apply ''observance''
(שְׁמִירָה) and ''fulfillment'' (עֲשִׂיָּה) to ordinances. For [up
till now,] Scripture had mentioned only ''fulfillment'' regarding
ordinances and ''observance'' regarding statutes (see previous verse).
- [Torath Kohanim 18:134]and live by them: in the World-To-Come. For if you say [that the verse refers to living] in this world, does he
not eventually die? [Torath Kohanim 18:134]I am the Lord: faithful to
pay a reward [an attribute represented by the Name ה ]. — [Torath
Palestine Targum renders Lev 18:5 as
And you shall keep My statutes, and the order of My judgments, which
if a man do he shall live in them, in the life of eternity, and his
portion shall be with the just: I am the Lord.
Following are some excerpts from an article on Book of Life
"[T]hree books are opened in heaven on Rosh Ha-Shanah, one for the
thoroughly wicked, one for the thoroughly righteous, and one for the
intermediate. The thoroughly righteous are forthwith inscribed in the
Book of Life, the thoroughly wicked in the Book of Death, while the
fate of the intermediate is suspended until the Day of Atonement"
(Rosh HaShanah 16b).
(Encyclopaedia Judaica, 1997 CD-ROM edition)
ספר הײם (Ps. 69:29, "book of the living"; so LXX., Vulg., R.V.
[margin]). The living are the righteous (second half of the verse),
who alone are admitted to citizenship in the theocracy. The wicked are
denied membership therein: they are blotted out of God's book (Ex.
32:32 et seq.). The figure is derived from the citizens' registers
(Ezek. 13:9; Jer. 22:30; and Ex. 32:30-34, accordingly assigned by
Holzinger to a late. stratum; see his commentary). The life which the
righteous participate in is to be understood in a temporal sense. In
Dan. xii. 1, however, those who are found written in the book and who
shall escape the troubles preparatory to the coming of the Messianic
kingdom are they who, together with the risen martyrs, are destined to
share in the everlasting life referred to in verse 2. The eternal life
is certainly meant in Enoch xlvii. 3, civ. 1, cviii. 3, and frequently
in the New Testament (especially in Revelation). The Targum (Isa. 4:3;
Ezek. 13:9) speaks of the "Book of Eternal Life." Temporal life is
apparently prayed for in the liturgical formula: "Inscribe us in the
Book of Life" (see Atonement, Day of). The Mishnah tells us that the
deeds of every human being are recorded in a book (Abot, ii. 1; see
iii. 16). The "Sefer Chasidim" (xxxiii.) pointedly adds that God is in
no need of a book of records; "the Torah speaks the language of man";
Paul also quoted Lev 18:5 in Romans 10:5 and Galatians 3:12
David Stern's Jewish New Testament commentary on Romans 10:5
5 The quotation is from Leviticus 18:5, “You shall therefore keep my
statutes and my judgments, which, if a person does them, he will live
by them.” Should there be any doubt whether the righteousness that
results from obeying God’s statutes and judgments leads to eternal
life, the verse says, “he will live by them,” on which Rashi (quoting
the Sifra, a fourth-century collection of midrashim related to
Leviticus), comments: “It refers to the world to come; for if you say
it refers to this world, doesn’t everyone die sooner or later?” Thus I
translate the phrase, he will attain life through them—eternal life.
The word for “live” or “attain life” is the same as that used at
8:12–13 to describe what will happen to the believer who “by the
Spirit” keeps “putting to death the practices of the body.”
Conclusion: Sha’ul affirms that the Torah and the Ruach HaKodesh offer
one and the same eternal life. This is consistent with and suggested
by the fact that the Holy Spirit came to the first believers on
Shavuot (Pentecost), the same day the Torah was given to Moses (see Ac
2:4&N). The two most important of the “statutes and judgments”
referred to in Leviticus 18:5 are stated by Yeshua at Mark 12:28–31:
(1) loving God (the Shema, Deuteronomy 6:4–5) and (2) loving one’s
neighbor as oneself (Leviticus 19:18). Both are predicated on trusting
in God: you can’t love God if you don’t believe in him as who he says
he is, and since both you and your neighbor are made in God’s image
you can’t love your neighbor as yourself in the sense that the Torah
demands without believing in the God who made both of you. Therefore,
Leviticus 18:5, quoted here by Sha’ul, backs up his point that obeying
the Torah requires trust, not legalistic works.
Notice especially this passage where Jesus implied that you must fulfill the law to inherit eternal life. The New Covenant was not instituted at that time.
(Luke 10:25-28) 25 And behold, a lawyer stood up to put him to the
test, saying, “Teacher, what shall I do to inherit eternal life?” 26
He said to him, “What is written in the Law? How do you read it?” 27
And he answered, “You shall love the Lord your God with all your heart
and with all your soul and with all your strength and with all your
mind, and your neighbor as yourself.” 28 And he said to him, “You have
answered correctly; do this, and you will live.”
(Matthew 19:16-19) 16 And behold, a man came up to him, saying,
“Teacher, what good deed must I do to have eternal life?” 17 And he
said to him, “Why do you ask me about what is good? There is only one
who is good. If you would enter life, keep the commandments.” 18 He
said to him, “Which ones?” And Jesus said, “You shall not murder, You
shall not commit adultery, You shall not steal, You shall not bear
false witness, 19 Honor your father and mother, and, You shall love
your neighbor as yourself.”