I've noted a couple times here Cave of Treasures. This was a Monophysite document... at first. By PseudoMethodius' time, Singar had a copy; Singar before it was Yezidi "Sinjar" was a Monophysite stronghold, like Mar Mattai and others too-close to Nineveh for Isho'yahb III's liking. PseudoMethodius although a Miaphysite himself did not push the issue, contrast his elder John bar Penkaye a decade earlier. Sergey Minov about a decade ago did a study; this came out of his thesis, so underpins his 2020 publication of said thesis.
First, a critique: one piece of evidence Dr Minov brings is the Bet Hale disputation. This is, since formal publication, considered an 'Abbasid-era text. It is too late for consideration in this argument. Now, on to happier content.
Minov relates that Singar at its founding hosted Monophysite exiles from Justin I. The Cave raises many Iranian tropes, not least the name "Peroz" for the wise men. Minov ponders if she hosted this book's very scriptorium.
But as it was copied in the Syriac Orient, Minov finds that the Cave suffered some intrusions, which went against its Monophysitism. In this time 'Abd al-Malik was weighing the scale for Monophysitism, going so far as to prevent the Church of the East from seating a "catholicos" pope. It may however be that Singar had access to the altered version as well. Some evidence that the Cave had trickled outside the boundary is John bar Penkaye, who used a parallel Jubal tradition. At any rate Singar dared use the Cave in an appeal to Melkites and even to Latins, two-qnômë stalwarts since Constantine IV.
This text assumes a cult of Christ's tunic. Minov sees this in Palaestinian / Jordanian churches over the later half of AD 400s.
The Cave proffers a legend of Solomon building Baalbek, which Baalbek's own touristry-department wasn't claiming as of AD 502. But we'll see it in pseudo(?)Zecharia of Mytilene. John of Ephesus is late enough I suspect he knew the Cave (Minov assumes Zuqnîn's several editors didn't interpolate the legend). That's a legend as could only come from a westerner.
Minov raises how Mono- is this text's physitism. Eutychian, that's how; or, so its critics following the councils of Ephesus rated it. (Later they will be called "Julianist", which as Minov points out is unfair to Julian.) The Cave didn't think Christ was circumcised in the flesh(!). Of course this note dropped out of the Eastern revisions but not fully, as by editorial-fatigue references slipped through later on. These "Phantasists" remained an embarrassment to Miaphysites in the early 500s, when Philoxenus of Mabbug/Manbij pens a rant against them. Minov uses that to date the original around that time. He might also have said around that city.
I do however think Minov is pushing the edge as he dates it around AD 600. I'd pin it much earlier, perhaps in Justinian's later years when - they say - he was leaning toward Eutychian "aphthartodocetism".