While reading through John R. (Jack) Levison’s The Spirit in First-Century Judaism I came across a quote from Seneca the Younger where in Letter 41 of his so-called “moral letters” he says the following:
“1. You are doing an excellent thing, one which will be wholesome for you, if, as you write me, you are persisting in your effort to attain sound understanding; it is foolish to pray for this when you can acquire it from yourself. We do not need to uplift our hands towards heaven, or to beg the keeper of a temple to let us approach his idol’s ear, as if in this way our prayers were more likely to be heard. God is near you, he is with you, he is within you. 2. This is what I mean, Lucilius: a holy spirit indwells within us, one who marks our good and bad deeds, and is our guardian. As we treat this spirit, so are we treated by it. Indeed, no man can be good without the help of God. Can one rise superior to fortune unless God helps him to rise? He it is that gives noble and upright counsel. In each good man
A god doth dwell, but what god know we not. ”
The language is intriguing. Seneca says that “god is near you” and that “a holy spirit indwells within us.” Then he shares a quote from Vergil, “A god doth dwell, but what god know we not.”  Seneca died in 65 CE, so it is altogether possible that he heard early Christians speaking of a holy spirit, but it is also possible that language about a holy spirit was more anthropological in most circles than theological.
At Qumran the Damascus Document describes those who has defiled the sanctuary at those who “have corrupted their holy spirit” (CD 5.11) and how the people of the covenant must “separate from all kinds of ritual impurity…not befouling each his holy spirit” (CD 7:3-4).  Now, there are at various points use of “spirit” language that seems to be about God in a way that detaches God from the human spirit shared by all—e.g., 2:12 speaks of God anointing the seers “by holy spirit”—but it is not uncommon for holy spirit to be the spirit of a moral or righteous person.
Similar language is found in 1QS where the Children of Light are differentiated from the Children of Darkness by “the spirit pervading God’s true society” which is “his holy spirit” (3:6-7). This spirit is from God, but possessed by the people of the covenant. Those who are outside of the covenant are not spirit-less, but they have been given (by God as well) an evil Spirit:
“He created humankind to rule over the world, appointing for them two spirits in which to walk until the time ordained fro his visitation. These are the spirits of truth and falsehood.” (3.17-18) 
The author describes the good spirit in similar language to Paul’s “fruit of the spirit” saying that this good spirit makes one to be full of “humility, patience, abundant compassion…” and much, much more (4:2-7). In 4.21 the people of the covenant are cleansed from their wicked deeds “by a holy spirit”. It is quite possible that the language used in these works has been influenced by Greek and Roman concepts of spirit, or vice versa, or some more complicated mixture.
 Seneca: Letters from a Stoic (and Biography) [Annotated] (Kindle Locations 872-878). Doma Publishing House. Kindle Edition.
 Aeneid, viii. 352
 trans. by M.O. Wise, M.G. Abegg Jr., and E.M. Cook, The Dead Sea Scrolls: A New Translation [Logos Edition]