I am currently reading up on of apocryphal and pseudopigagraphical literature, and I see on a list that the Testament of Hezekiah is enumerated as one of them. However, I cannot locate a source or any short blurb on its date, origin, and content? Do any of you know? Thanks!
After a bit more research, I found reference to the "Testament of Hezekiah." It appears, that it's a component of the larger pseudegraphical text, "Ascension of Isaiah." Perhaps why I couldn't find info at first, is that it is regarded as a "Christian text" -- though it is believed to have had Jewish origins, but was redacted by later Christians.
Theories for its dates from 1st to 3rd centuries CE. It may actually be a compilation of multiple texts that were composed at different times and later compiled together.
The overarching content of the "Ascension of Isaiah" concerns the martyrdom of Isaiah, wherein Isaiah warns King Hezekiah that Manessah (the next in line) will not continue to reign in righteousness. Once Isaiah's prophecy proves to be true, Isaiah and other prophets flee to the deserts for safety. Unfortunately, they are encountered by a false prophet, Belkira (inspired by the infamous demon, Beliar), and charges Isaiah of treason, and Manessah condemns Isaiah to death, which Belkira carries out. (Later, Isaiah ascends into the 7 heavens, etc). This is the "Ascension of Isaiah." These are the sections believed to have Jewish origins (with the parallels of the demon Beliar also being present in the Book of Jubilees, fragments found in Qumran of the Testaments of the 12 Patriarchs, and the Sibylline Books. The other proposed Jewish parallel is the method of Isaiah's death -- being sawed in half -- as accounted for in both the Jerusalem and Babylonian Talmuds).
As for "The Testament of Hezekiah" (and back to the question at hand) -- it is projected into the middle of the "Ascension of Isaiah." This is the blatantly Christian portion of the text as it concerns a vision of Christ's "future" coming, the downfall of the Christian church due to corruption, the dreadful reign of Beliar (the demon), and ultimately the "Second" Coming. Some scholars think there are clear codes pointing to the persecution of the Church by the Roman emperor, Nero (which early Christians thought was the antichrist).
Anyway, I'm sorry for not finding this info before I posted the question, and thinking it was largely a Jewish text when it is actually a hybrid of Jewish and Christian texts. For those interested (if any), the information was located in James H. Charlesworth's "Old Testament Pseudepigrapha" (Hendrickson Publishers, 2010).