The phrase "the while" indicates the pending passage of an indefinite period of time. "The While" is a nebulous (fuzzy) term, not meant to be precisely interpreted in the sense of "starting here and ending here". Instead, the phrase suggests a vague notion of unfolding time.
The author could have written instead: "stands over you from now on" or "stands over you forever after", and kept the same meaning.
Poets and pundits tend to use this type of language, but you would not hear it in ordinary, everyday speech.
You will also hear the phrase "all the while" used in the same manner. For example, "He was all the while looking forward to seeing her", suggesting that his anticipation was ongoing, and that he will be continually looking forward to seeing her throughout his present state of mind / activity.