How do Trinitarians who argue the 'ego eimi' at John 8:58 ought to be translated 'I AM' explain the lack of reactions to the same phrase?

In John 9:9, the man is responding to the question "Is this not the man who used to sit and beg?" The words "I am" in that context are thus understood as a verbal abbreviation of "[yes,] I am [that man]".

In John 8:58, as noted in eques' answer, it makes much less sense for there to be an implicit 'him'/'he'. The most obvious 'target' for such would be Abraham, but then Jesus would be saying "before Abraham was [born], I was Abraham"... which seems very strange. Is Jesus Abraham reincarnated? Another possibility is that Jesus was speaking earlier of his Father, which doesn't help matters, since in that case, while we might not render his statement "I Aᴍ", it would thus be "I am the Father", which is essentially the same thing.

To be honest, what I find interesting is that John 8:24 has the same problem. While John 8:58 has the further problem that adding an implied "he" is arguably worse grammar, in John 8:24 it is very unclear what the target of the added "he" should be, which leads me to wonder if that verse as well ought to be translated "I Aᴍ". (To be clear, I'm not saying it's impossible to presume what "he" might be implied, just that it's very unclear.) This might even apply to John 8:28, although at least there is seems conceivable that the implication is "I am [the Son of Man]"... but again, it might also be properly interpreted as "I am [He who sent me]" (i.e. the Father).

It's also worth noting that we don't have an exact transcription of Jesus' words (which were presumably not Greek). It's not inconceivable that He actually used "יהוה‎", or an Aramaic equivalent, which the author chose to translate as "ἐγώ εἰμι".

Jesus' arguments escalate and culminate in violent reaction in 8:58

Throughout the entire chapter, Jesus says ego eimi in ever more unambiguous ways, in the face of angrier opposition. When He says it unambiguously, only then is he violently attacked.

From the Jews' point of view: In 8:24, there is confusion about what Jesus is claiming, including but not limited to His use of ego eimi. So the reaction is to ask for clarification (8:25). 8:27 states this explicitly; they didn't realise that Jesus was talking about the Father.

8:28 has Jesus using his title of the Son of Man, explicitly mentioning the Father, and again using ego eimi.

Finally, the claim to have existed before Abraham in 8:58 is so obviously a claim to deity as to provoke violent opposition.

It's a perfectly ordinary progression from debate, to argument, to heated controversy that we often observe when someone clarifies their stance and it turns out to be more radical than initially thought. See any politics forum!

From our point of view: In terms of hermeneutic, we work backwards: 8:58 and its immediate context stands alone as a claim of deity; there's no other way to interpret claiming to have existed before Abraham, let alone using a theologically loaded term for the third time (people notice repetitions and there's an implication of equal intent that comes with it).

8:28 could possibly stand alone as a claim to deity with just its immediate context, but is interpreted in light of 8:58.

8:24 is supported by the other two usages and the triadic repetition, but wouldn't have stood alone.

The literal meaning of "ego eimi" is simply "I am" (Ego = I; eimi = am).

It is not "I am he" or "I am the one" or so on. That is, the original Greek contains no elements which imply those extra words or their meanings universally.

Notably, "I am" only implies the divinity in some contexts, just as not every use of "I am" in the Old Testament implies "I AM" as in Exodus. Thus, Trinitarians would not assert that the use of "Ego eimi" (translated as "I am he" or "I am the one") in John 8 is Christ indicating his divinity, which is also demonstrated by the fact that some other than Christ (whom no one thinks is divine) uses the exact phrase in John 9:9.

The question then is why is "Ego eimi" in John 8:58 understood as referring to the divinity (and thus capitalized as "I AM" in many modern editions).

Grammatically, we have an odd sentence: πρὶν Ἀβραὰμ γενέσθαι ἐγὼ εἰμί -- Before Abraham was, I am. The verb translated as was is also in the past in Greek (Aorist to be precise) and yet the sentence places a present event ("am") before something that happened (aorist = a simple complete event). This only makes sense if it refers to someone eternal, hence divine. Secondarily, because the Jews try to stone him after this, we can infer that they understood him as saying something blasphemous since blasphemy was punished by stoning.