A Study of Other Uses with ἐν in the NT
There are 6 or 7 occurrences using ἐν in Scripture related to πιστεύω1 (depending on textual variant, which occurs in the verse in question), compared to roughly 46 using εἰς (I did not check for variants in these, hence "roughly") which are noting the thing/person that is believed (i.e. the content of what is believed).2
Those instances of ἐν occurring are instructive, because they all can be considered as instrumental or locative use of the dative.3 Only the relevant portion of the verse is given below (MLT = "my literal translation")
Mark 1:15 (no variants)
μετανοεῖτε, καὶ πιστεύετε ἐν τῷ εὐαγγελίῳ
Repent, and believe in the gospel (MLT and NKJV)
Jesus is speaking here, and using the imperative form πιστεύετε to command action. The "gospel" being referenced here by Jesus is the "good news" that immediately proceeded this command, "The time is fulfilled, and the kingdom of God is at hand" (NKJV). For purposes here, there is no need to get into the discussion of what exactly "the kingdom of God" is, nor what is meant by the "time is fulfilled." What is important to see is that this message is the referent for the "gospel," and so "believe in the gospel" is effectively saying, "believe God's promise of the kingdom is at hand by my announcing of this good news." In other words, the object of belief (or "content" of belief) was in the promise of the kingdom, but the instrumental vehicle pronouncing this was the declaration of it, the declaration of good news.
Jn 16:30 (no variants)
ἐν τούτῳ πιστεύομεν ὅτι ἀπὸ θεοῦ ἐξῆλθες
By this we believe that from God you came out (MLT)
By this we believe that You came forth from God (NKJV)
Note here that both ἐν and a ὅτι clause are used together with the verb. The ὅτι is giving the direct object of the content of belief, that Jesus "came forth from God." The ἐν is giving instrumentality, by what means they believe it. The demonstrative pronoun τούτῳ points to this means by which they believed, namely that they already believed that Christ "knows all things" and has "no need that anyone should question" Him (first part of v.30), and He had just declared He came from God (vv.27-28). So because the disciples believe Who Christ is, then by means of His testimony alone, "by this," His mere assertion, they believe the content of what was stated.
Rom 10:9 (no variants)
καὶ πιστεύσῃς ἐν τῇ καρδίᾳ σου ὅτι ὁ θεὸς αὐτὸν ἤγειρεν ἐκ νεκρῶν
and believe in the heart of you that - God Him He raised from [the] dead (MLT)
and believe in your heart that God has raised Him from the dead (NKJV)
This is the second of two parts noted in order that one "will be saved," the other part being "if you confess with your mouth the Lord Jesus" (NKJV). Notice again the ἐν used with a ὅτι clause. That clause is the content of what is believed, and the ἐν is then either instrumental (the heart is the means of evoking the belief) or locative (the heart is the location of belief, as compared to merely the mind).
Eph 1:13 (no variants)
This one is a bit trickier, as there are two possible options for translation that would indicate two different things, but given the pattern so far, I lean toward option #2 (see discussion that follows):
ἐν ᾧ καὶ πιστεύσαντες
OPT 1 - in whom also having believed (MLT and NKJV)
OPT 2 - by which also having believed (MLT)
The ambiguity resides in the relative pronoun ᾧ that is the object of the second ἐν preposition in the verse.
The first ἐν ᾧ starts v.13 and therefore immediately follows v.12 that ended with ἐν τῷ χριστῷ ("in the Christ," MLT), and so "in whom" (KJV) or "in him" (ESV/NKJV/NASB) are correct for the first instance, as the relative pronoun is referring back to the preceding referent, which is Christ.
However the second ἐν ᾧ of the verse could be (1) a masculine singular reference back to Christ, and thus "in whom" (KJV/NKJV) or "in him" (ESV) is who was believed in, which would be functionally equivalent to εἰς αὐτὸν. If so, this would then be the first use of ἐν so far in this study for declaring content of what is believed. But it could be (2) a neuter singular reference back to the preceding referent, which is the participle phrase:4
ἀκούσαντες τὸν λόγον τῆς ἀληθείας, τὸ εὐαγγέλιον τῆς σωτηρίας ὑμῶν
having heard the word of the truth, the gospel of the salvation of you (MLT)
after you heard the word of truth, the gospel of your salvation (NKJV)
This seems to be how the NASB and NIV take it, as both actually leave the ἐν ᾧ phrase untranslated, but tie the belief more directly to the preceding participial phrase (especially the NASB):
after listening to the message of truth, the gospel of your
salvation—having also believed (NASB)
when you heard the message of truth, the gospel of your salvation. When you believed (NIV)
In essence these translations are indicating the gospel again is the instrumental vehicle "by which" these believers Paul is writing to are "having also believed." This would make the dative ἐν ᾧ with the πιστεύσαντες match the pattern previously seen of showing the instrument by which belief came.
1 Thes 1:7 (has a nearly insignificant variant)
There is a textual variant here that has a second ἐν before τῇ Ἀχαΐᾳ, which would not change the meaning:
πᾶσιν τοῖς πιστεύουσιν ἐν τῇ Μακεδονίᾳ καὶ [ἐν] τῇ Ἀχαΐᾳ
to all the ones believing in - Macedonia and [in] - Achaia (MLT)
to all in Macedonia and Achaia who believe (NKJV)
The ἐν here is not actually in relation to our verb, πιστεύουσιν, directly, but to the locative place of where "all the ones believing" are residing. It is the location of those being referenced as believing. So this ἐν is irrelevant to the investigation here as it does not relate either to the object of belief or the means there of.
1 Tim 3:16 (no variant at this location)
ἐπιστεύθη ἐν κόσμῳ
was believed in the world (MLT)
Believed on in the world (NKJV)
This use is similar to 1 Thes 1:7, as the ἐν is describing the location of where "God" who "was manifested in the flesh" (noted toward the beginning of v.16) was believed, "in the world." So it too does not relate to either the content of the belief or the means.
The John 3:15 Use
The majority text has εἰς αὐτὸν at John 3:15, whereas the UBS/NA text has ἐν αὐτῷ, which Metzger rates by the UBS text critical standards as "almost certain" (Disclaimer, I tend toward majority text readings and use differing text critical rules than Metzger, et. al., so in my view, most likely εἰς αὐτὸν is correct in v.15, nevertheless...). He states of the verse:
Exegetical as well as textual problems are involved in deciding among
the variant readings. Except for this passage, the fourth evangelist
always uses εἰς after πιστεύειν (34 times), never ἐν. On the other
hand, if ἐν αὐτῷ is original here, the meaning may well be, “that
every one who believes shall in him [i. e. resting upon him as the
cause] have eternal life.” In support of such an interpretation is
John’s manner of placing an adverbial phrase with ἐν before its verb
when the phrase is emphatic or metaphorical (cf. 5:39; 16:33; and 1 Jn
passim). On balance, therefore, the reading of P75 B al, being
ambiguous, seems to account best for the rise of the other readings.5
However, if the minority reading ἐν αὐτῷ is correct, the NT evidence discussed above points strongly toward ἐν showing instrumentality (or in a personal sense, agency). The interpretation would then lean toward something like this:
ἵνα πᾶς ὁ πιστεύων ἐν αὐτῷ ἔχῃ ζωὴν αἰώνιον
in order that all the ones believing by him will have life eternal (MLT)
The idea being that Christ is not only the ultimate content of belief (v.16 with εἰς αὐτὸν) but also the ultimate instrument or agent of belief arising.
However, given that this reference follows the v.14 note that "the Son of Man be lifted up," (NKJV) and also given that there is again ambiguity with αὐτῷ (it can be a masculine or a neuter singular), then the translation could be the neuter "by it," referring to the instrumentality of the event of lifting up of the Son as the means by which one comes to believe "heavenly things" (v.12). This would parallel the typology established in v.12 of Moses lifting the serpent up as the means by which Israelites believed God and were saved from the snake bites (Num 21), so too God is lifting up Christ on the cross as the means by which "whoever" believes God will be saved.
Note that all these ideas of what it "could" mean are valid theologically: (1) Christ's crucifixion is a means for people to believe, (2) Christ Himself in incarnating and dying is an agent of bringing belief, and (3) Christ is the one to believe in for obtaining eternal life.
If the minority ἐν αὐτῷ reading is correct (which is suspect), then evidence suggests it refers to some form of instrumentality in one coming to faith, rather than what εἰς αὐτὸν refers to, the content of faith.
1 I purposely state "related" because as analysis will show, these are not normally expressing the object to which one is believing.
2 This is the typical way such is expressed, as expressed in William Arndt, Frederick W. Danker, and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000), s.v. πιστεύω 1.a.α.
3 "Instrumental" indicates the instrument (or agent, if a person) by which means something comes about. "Locative" indicates the place at or in which something occurs. See Daniel B. Wallace, Greek Grammar Beyond the Basics: An Exegetical Syntax of the New Testament (Grand Rapids, MI: Zondervan, 1996), 153-155 (for locative or "local"), and 162-166 (for instrumental and agency).
4 Of relative pronouns, it may have "the neuter gender under the influence of an abstract idea implied in the entire statement," see H. E. Dana and Julius R. Mantey, A Manual Grammar of the Greek New Testament, (Upper Saddle River, NJ: Prentice Hall, 1957), 126.
5 Bruce Manning Metzger, United Bible Societie, A Textual Commentary on the Greek New Testament, Second Edition a Companion Volume to the United Bible Societies’ Greek New Testament (4th Rev. Ed.) (London; New York: United Bible Societies, 1994), 175.