Disclaimer: Because the question asks about "academic methodology", I am simply writing how I went through and interpreted this passage, applying some of those exegetical standards. Obviously, people can use the same methods to come to different conclusions - but this shows how I came to my own.
1. Question Restatement
In Hebrews 4:9, what does the word "σαββατισμὸς, sabbatismos" mean, and what is the methodology to interpret / translate this word?
Hebrews 4:9, NASB- So there remains a "Sabbath rest, (σαββατισμὸς)" for the people of God.
Note: The quickest / most elegant answer to this, is to observe that "Sabbath [rest]" is singular, and NOT plural. It does not say, "there remains [multiple] Sabbath [rests]", but rather, "their remains [A] Sabbath [rest]."
It is often argued, (e.g, Sabbatismos: Does Hebrews 4:9 Teach Rest on the Sabbath?) that this passage serves as a "proof-text" that Christians must observe the Mosaic Commandment for a Sabbath Rest. Two main proofs are cited for this:
Professor Andrew T. Lincoln states, “The use of sabbatismos elsewhere in extant Greek literature gives an indication of its more exact shade of meaning. It is used in Plutarch, De Superstitione 3 (Moralia 166A) of Sabbath observance. [... and other examples] ...
Falsified: All of those were written well after the Book of Hebrews which was written while the temple was still standing. Even the quote from Plutarch seems erroneous, (See Greek Lexical Semantics, below).
The truth is, the Sabbath is considered as a type. All types are of full force till the thing signified by them takes place. (ibid.)
Falsified: Following James' judgment in Acts 15:13-31, Christians rejoiced BECAUSE they were freed from those requirements, (like circumcision, which is certainly a "type" of something to come).
2. Quick Answer - Defer to the Author's Own Explanation:
There is no need for theological or linguistic gymnastics when the writer explains themselves.
The only reasonable interpretation is to accept the writer's own explicit explanation that Israel, (even Moses), never actually observed the Sabbath rest as intended by God, (and even Christians still hadn't).
In addition to the academic observations, (see following sections), of language and syntax, the single most important standard is to always defer to a writer's own explanation. A writer's personal explanation supersedes any academic presumptions, in all cases.
Fortunately, the writer of the Book of Hebrews DOES provide their own explanation, explicitly - which also affirms standard linguistic observances.
3. The Context the Author Provided - Even Moses Never Observed the Sabbatismos:
English translations inject the word "rest" into the text of Hebrews 4:9, Interlinear, which is valid - given that the author uses "rest" 11 times within the immediate context alone, (See Hebrews 10-11, "Rest", Interlinear). Whatever Sabbatismos means, in this context, Sabbatismos must be understood in terms of "Rest", a greater "Rest" than even Moses observed.
If the writer was speaking of a "weekly Sabbath rest" as commanded by Moses - they could not - in the same breath - write it was never observed by Israel, let alone Joshua or Moses:
NASB, Hebrews 4:8 - For if Joshua had given them rest, He would not have spoken of another day after that. 9 So there remains a Sabbath rest for the people of God. 10 For the one who has entered His rest has himself also rested from his works, as God did from His.
Therefore, the writer of the Book of Hebrews was clearly making a distinction between the "Weekly Sabbath" that Moses actually observed, and a "Sabbatismos" that neither Moses, Joshua, nor any in Israel ever entered into.
The immediate context and the entire book are about prophecy:
Readers cannot reasonably dismiss the immediate context, (and the intent of the book) which is plainly speaking in prophetic terms, and how Jesus fulfils messianic prophecy and the necessity to be Christian - in order to observe a Sabbath Rest that will come, for all.
4. Christianity as taught by Jesus and the Apostles:
This writer, Paul, and even Jesus, show that observance of the "Weekly Sabbath" (as required by the Pharisees), and "The Sabbatismos" require mutually exclusive standards. That is, it would be pointless to observe a weekly Sabbath, if the true Sabbath Rest, (The Sabbatismos), is forfeited.
Even in my own life, I have never witnessed, (anywhere I have been in the world), a Rabbinically observed Sabbath where people actually rested from labor. They merely exchange one form of labor for another. In fact, religious Jews usually appear far more excited when the Sabbath is over, (rushing for cigarettes, relieved of Sabbath obligations, exhausted from their preparations, etc.). The "mutually exclusive" part about all of this is the Rabbinic mandate to force all of their requirements as a burden upon others, (an oppression), although they wouldn't even do this to their own animals:
NASB, Luke 13:14-16 - ... “There are six days in which work should be done; so come during them and get healed, and not on the Sabbath day.” 15 But the Lord answered him and said, “You hypocrites, does not each of you on the Sabbath untie his ox or his donkey from the stall and lead him away to water him? 16 And this woman, a daughter of Abraham as she is, whom Satan has bound for eighteen long years, should she not have been released from this bond on the Sabbath day?”
Jesus' rationale makes sense: if people are more favoured than animals, by God, then their rest should be far more fulfilling. If peoples' rest is not more fulfilling than what animals receive, then it is obviously not the rest that God desires to bless people with.
A Christian writer would not, at all, presume to bind Christians under Pharisaic standards and law, (whom Jesus declared a "Synagogue of Satan"). If this writer had been saying "Christians are required to observe the weekly Sabbath", they would have said "how to", otherwise it could only be assumed the writer was advocating Pharisaic requirements (which Jesus condemned) - which creates a contradiction that invalidates the whole of Christian Scripture.
In fact, all judgments about weekly Sabbath and festival observances were expressly prohibited within Christianity. If the writer of the Book of Hebrews were contradicting this, it would have created a huge amount of confusion:
NASB, Colossians 2:16 - Therefore no one is to act as your judge in regard to food or drink or in respect to a festival or a new moon or a Sabbath day—
5. Author's Writing Style:
The writer of Hebrews is very philosophic, consistently writing about "abstractions" and "spiritual" ideas that are only vaguely represented in Human practice, "forms and shadows". If the writer had been affirming weekly Sabbath observance, they would have explained "how to", by writing more practically, and less philosophically:
NASB, Hebrews 8:5 - who serve a copy and shadow of the heavenly things, just as Moses was warned by God when he was about to erect the tabernacle; for, “See,” He says, “that you make all things according to the pattern which was shown you on the mountain.”
The writer of Hebrews never uses the word for "Sabbath", (see Concordance Entries), except for this one very unusual morphological instance. Although, Hebrews 4:4 speaks about God's rest, nowhere does the author write about any practices of observance, by people.
6. The audience of the Book of Hebrews:
The Book of Hebrews was certainly written to Christians, who were at least knowledgeable of Hebrew Scripture as presented by Jesus, John the Baptist, and the Apostles. This likely included Hebrews in the diaspora, Galilee, Samaria, and other communities that had rejected "institutional" forms of Judaism, (like Pharisaism and Sadducean Judaism). The only reasonable explanation that the improvisation of "sabbatismos" might even have been necessary, is if - and only if - injecting a sense of "abstractness" would help clarify what they were trying to say.
At that time, Sabbath observance requirements were not at all "uniform" - certainly not within the Galilee. Sabbath observance was a point of huge contention within Judaism (let alone Christianity), and the author would have certainly known this. If they were going as far to tell Christians that a weekly Sabbath must be observed, they would have certainly said "how to".
7. Etymology and Morphology:
Sabbatismos" originates from the Hebrew word for "seven":
Exodus 16:26, NASB - Six days you shall gather it, but on the seventh day, the sabbath, [שַׁבָּ֖ת, Shabbat], there will be none.”
Morphologically, "-ισμὸς" implies an abstraction:
Because the writer appended "-ισμὸς" as the suffix, Greek readers, at the time the book of Hebrews was written, would have reasonably inferred that the author was speaking of the "sabbath" in an abstract, philosophical, or spiritual sense.
Wikipedia, "-ism" - Ultimately from either Ancient Greek -ισμός (-ismós), a suffix that forms abstract nouns of action, state, condition, doctrine; from stem of verbs in -ίζειν (-ízein) (whence English -ize), or from the related suffix Ancient Greek -ισμα (-isma), which more specifically expressed a finished act or thing done.
The morphology of "
σαββατισμὸς" indicates that "
σάββατον" is not being conformed to fulfill a grammatical requirement, (plurality, part of speech, etc.), but rather the morphology indicates that the author is "extending" the base meaning of the word, by injecting another sense on top of it. Specifically, the morphology indicates that the author is indicating a more "abstract" sense of how the word is normally interpreted.
8. Hebrew Lexical Semantics:
Sabbath" originally referenced God's Rest on the seventh day of creation, (Exodus 20:11). Even Moses' commandment for people to rest, was to be a memorial for people to remember God's own rest:
NASB, Exodus 20:11 - For in six days the Lord made the heavens and the earth, the sea and all that is in them, and rested on the seventh day; therefore the Lord blessed the sabbath day and made it holy.
Sabbath", is a Hebrew figure of speech, not a Greek one, (see Σάββατον @ logeion.uchicabo.edu, and variants). As a figure of speech, it's actual meaning is distinct from its literal meaning ("
seventh"), but it rather connotes "a period of rest", a reprieve from labor. Most specifically, it implies a release from a burden, (even for cattle; Exodus 20:10) - the burden that labors are subjected to judgment for good or ill, (even God's day of rest was not pronounced "Good").
NASB, Genesis 1:31 - God saw all that He had made, and behold, it was very good. And there was evening and there was morning, the sixth day.
Note: Although God's own work was subjected to judgment, no judgment, for good or ill, was pronounced for the 7th day.
However, throughout Scripture, it is clear that "Sabbath" is a figure of speech for "Rest from Labor". "Sabbath" was not intended to be limited to "seven day periods", evidently because several other days were considered Sabbaths, not just "Saturdays". (See Special Shabbat, Wikipedia.) That is, it isn't the superstition that the "number seven" makes a day holy, but it is God's declarations that determine what is to be holy, or not. It's not a function of math or superstition.
9. Greek Lexical Semantics:
Sabbath, is a Hebrew figure of speech, not a Greek one, (see Σάββατον @ logeion.uchicabo.edu, and variants).
Sabbatismos is not a word found in Greek texts until well after the Book of Hebrews was written substantiating this was a "new" and exclusively Christian idea, (apparently not even used by Josephus). The only exception to this appears to be a manuscript error in Plutarch, De Superstitione 3, in Moralia 2. 166a. Did Plutarch Use the Term Sabbatismos in Plutarch, De Superstitione 3, in Moralia 2. 166a
If any prior or current instance is found, then the validity of this answer is not "strong" and unsound, (Wikipedia, Logic: Soundness).
Note: In fact, I have had to update this because of a [probably] invalid claim that Plutarch used this term, (see the opposing answer).