In this sense, "quarter" or "quartering" derives from traditional nautical practice, such as in
www.seatalk.info/cgi-bin/nautical-marine...default&Term=quarter.
That is, if you are pointing north, say, a quartering wind is coming from either the SE or SW or, more appropriately, the SE or SW quarter.
Strictly, an expression such as. "a quartering tailwind" is a tautology as quartering relates to the stern or tail. The appropriate expression is, simply, "a quartering wind".
Having said that, you will see references to quartering winds from the forward quadrants - the joys of English as a living and changing language, I guess. If you choose to say "a quartering headwind (or tailwind)" we all are going to know what you mean.