I suppose that holding the brush suspended neutralizes the r/l issue for Chinese characters in very formal contexts. Some older Korean goes down from the right edge, not across (as also some Japanese and Chinese writing, if I'm not mistaken), but I have always wondered how the writing implement was held for small glyphs written close together down-from-left in codices. [ETA or perhaps I'm wrong and it's down from right in codices, too.] For Koreans, at least through the 1970s there was some attempt to make lefties write righty and hide their putative misfortune.

Add Mongolian script to your grant proposal list?--vertical, left to right, but the vert aspect may or may not have some effect upon ductus.