Probert, A New Short Guide to the Accentuation of Ancient Greek
(Bristol Classical Press 2003) discusses the paroxytone accentuation of ἔστι (sec. 282, pp. 144-6).
To summarize, the argument that ἔστι was paroxytone when it expressed existence or possibility and could not be omitted (as well as when it was the first word in a sentence or verse, or followed certain function words) was formulated by Hermann (1801), based on a statement attributed to Herodian (2d century CE), as well as some obscure remarks by the Byzantine scholars Photius (9th c.) and Eustathius (12th c.). (Most of what we know of Herodian's work on Greek accentuation is derived from the scholia found in the 9th or 10th century ms. of Homer, the Codex Venetus, or "A".)
Wackernagel (1877) challenged Hermann's view, asserting that the paroxytone accentuation was only determined by position, not by meaning, based on historical linguistics. W.S. Barrett's edition of Euripides' Hippolytus
discusses the point (App. II, pp. 425-6), coming down in favor of Wackernagel. M.L. West, in the preface to his Teubner edition of Aeschylus, also adopts Wackernagel's position (p. xxxi).
Barrett outlines Wackernagel's argument, which I haven't been able to obtain access to. Basically, comparative Indo-European linguistics show that finite verbs were originally enclitic, except when in sentence-initial position. Eventually finite verb-forms acquired recessive accent in Greek, except for most of the present-tense forms of εἰμι and φημι, but, in Wackernagel's view, these continued to be accented in word-initial positions and after οὐ, based on position, not meaning. (There is also a dispute as to whether ἔστι is paroxytone after function words other than οὐ.) That's a very inadequate summary of the argument, but I'm sure that Wackernagel's discussion, which I haven't seen, would have much fuller and more compelling than I'm able to frame it.
You can find a discussion of Hermann's position in Chandler, p. 267.https://archive.org/stream/accentuationgree00chanuoft#page/266/mode/2up
The lesson from all this is that the "rules" of ancient Greek accentuation, especially the more obscure points, should be treated with a certain amount of skepticism.