I saw a few bits here and elsewhere on it, but I have yet to find something that explains its usage, in detail(e.g. in positive and negative contexts and in different tenses). Anyone know?
While I'm sure the underlying grammar makes the analogy a rather liberal one, I have always tended to feel that these were similar to patters in English that use "be". That is, an old form of the subjunctive:
Be it A, or be it B, it's fine regardless.
Whichever it be.
Whatever the case be.
The pattern can always (well, usually) be reworded using も to mean essentially the same thing.
なんせ* (no strict conversion; maybe 何が何でも)