Looking it up (on wiktionary, at least) it seems like originally 又 was "right hand", however if you look at really old versions of that character it looks mostly like a mirror of 𠂇.
Interestingly, Wiktionary lists both left and right as phonosemantic compounds where the phonetic part is "left hand" or "right hand" and the semantic part is "assist" and "mouth" (I think in this case the "mouth" is used to bolster the "pronounced like" of the phonosemantic compound, since it's used on the right side not the left). This seems to be because the word for "left hand" became the word for "left" and same for "right hand", so they're pronounced the same; and the semantic component was added later to bolster/specialize the glyph.
Anyway, it seems like the 𠂇 radical in 右 is etymologically a variant of 又 which is a mirror of 𠂇 (well, a mirror of a three-pronged historical form of that) except it was rotated around the glyph so that it looks exactly like 𠂇 but the stroke order is reversed.