Second Death in Jewish Targums (aka Targumim) and Philo

Harry Sysling in Tehiyyat Ha-metim : The Resurrection of the Dead in the Palestinian Targums of the Pentateuch and Parallel Traditions in Classical Rabbinic Literature, has the most comprehensive treatment on the second death in the Targumim -- at least the most comprehensive that I was able to find.

He analyzes:

• Targum Onqelos of Deut 33:6 (p. 211)
• The Palestinian Targumim of Deut 33:6 (p. 214)
• The second death in the Targum of the Prophets (tgYon) (p. 219)
• The second death in the Targum of the Psalms (p. 221)

He also considers Greek sources including the Apocalypse of John (as well as other rabbinical tradition). 

Sysling's summary offers at least the following various usage of "the second death":

• as the death by which the wicked die;
• the retribution in Gehinnom "which burns all day long";
• as exclusion from life in the world to come (and from the resurrection?);
• as identical with the punishment in Gehinnom; and
• as exclusion from the resurrection.

Sysling's comments seem essentially consistent with those of the great Calvinistic Baptist author, John Gill.  John Gill, commenting on Revelation 2:11, states:

shall not be hurt of the second death; by which is meant eternal death, in distinction from a corporeal and temporal one; and lies in a destruction of both body and soul in hell, and in an everlasting separation from God, and a continual sense of divine wrath; but of this the saints shall never be hurt, they are ordained to eternal life; this is secured for them in Christ, and he has it in his hands for them, and will give it to them. The phrase is Jewish, and is opposed to the first death, or the death of the body; which is the effect of sin, and is appointed of God, and which the people of God die as well as others; but the second death is peculiar to wicked men. So the Jerusalem Targum on Deuteronomy 33:6; paraphrases those words, "let Reuben live, and not die," thus; "let Reuben live in this world, and not die anyynt atwmb, "by the second death," with which the wicked die in the world to come." Of which sense of the text and phrase Epiphanius makes mention {q}. See the same phrase in the Targum of Jonathan ben Uzziel, in Isaiah 22:14; and in Jeremiah 51:39; and in Philo the Jew {r}.

{q} Contr. Haeres. Haeres. 9. 

{r} De Praemiis & Poenis, p. 921.

Baker's Evangelical Dictionary of Biblical Theology, includes, within its entry for "Second Death" the following:

This phrase is found only in Revelation 2:11,20:6,20:14 , and 21:8. The Targums use it (Deuteronomy 33:6; Psalm 49:11 ). Philo uses the term to refer to all miseries arising from sin causing physical death followed by hopelessness in the afterlife (Rewards and Punishments 2.419). Revelation 2:10-11 contrasts it with the life given to the faithful. Death is the loss of the only kind of life worthy of the name.

Section XII of Philo's "Rewards and Punishments" has the following account:

XII. (67) Therefore those rewards which were thus long since assigned to the good, both publicly and privately, have now been described though somewhat in outline, but sufficiently to enable anyone to comprehend with tolerable ease what has been omitted. We must now proceed in regular order to consider in turn the punishments appointed for the wicked, speaking of them in a somewhat general way since the time does not allow of my enumerating all the particular instances. (68) Now there was at the very beginning of the world when the race of men had not as yet multiplied, a fratricide: this is the first man who ever was under a curse; the first man who imprinted on the pure earth the unprecedented pollution of human blood; the first man who checked the fertility of the earth which was previously blooming, and producing all kinds of animals, and plants, and flourishing with every kind of productiveness; the first man who introduced destruction as a rival against creation, death against life, sorrow against joy, and evil against good. (69) What then could possibly have been inflicted upon him, which would have been an adequate punishment for him, who thus in one single action left no description of violence and impiety unperformed? Perhaps some one will say he should have been put to death at once; this is a human mode of reasoning, fit for one who does not consider the great tribunal of all for men look upon death as the extreme limit of all punishments, but in the view of the divine tribunal it is scarcely the beginning of them. (70) Since then the action of this man was a novel one, it was necessary that a novel punishment should be devised for him; and what was it? That he should live continually dying, and that he should in a manner endure an undying and never ending death; for there are two kinds of death; the one that of being dead, which is either good or else a matter of indifference; the other that of dying, which is in every respect an evil; and the more protracted the dying the more intolerable the evil. (71) Consider now then how it is that death can be said to be never ending in this man's case; since there are four different affections to which the soul is liable, two of them being conversant with good either present or future, namely, pleasure and desire; and two with evil either present or expected, namely, sorrow and fear; it cuts up the pair of those which are conversant with good by the roots, in order that the man may never receive pleasure from any accident of fortune, nor ever feel a desire even for anything pleasant; and it leaves him only those affections conversant about evil, sorrow without any mixture of cheerfulness, and unmingled fear, (72) for the scripture Says{2}{#ge 4:14.} that God laid a curse upon the fratricide, so that he should be continually groaning and trembling. Moreover he put a mark upon him, that he might never be pitied by any one, so that he might not die once, but might, as I have said before, pass all his time in dying, amid griefs, and pains, and incessant calamities; and what is most grievous of all, might have a feeling of his own miseries, and be afflicted both with the evils which were before him, and also from a foresight of the number of misfortunes which were constantly impending over him, which nevertheless he was unable to guard against, since hope was wholly taken from him, which God has implanted in the race of mankind, in order that thus, having an innate comfort in themselves, they might feel their sorrows relieved, provided they had not committed any inexpiable crimes. (73) Therefore, as a man who is being carried away by a torrent shudders at the nearest waves by which he is being hurried away, and still more at those coming upon him from above, since the one is continually and incessantly propelling him forward with violence, but the other being raised above him threatens to overwhelm him utterly, so in the same manner those evils which are present are grievous, but those which proceed from fear of the future are more grievous still; for fear continually supplies sorrowful feelings as from an everlasting spring.

I would love to agree that Philo "uses the term" or "the same phrase" but I do not see it. That said, he does seem to discuss two senses of "death," one of which fits quite well with Johannine theology.