I think you can forget that definition "something done together". That's simply an over- (or false-) generalization. And is basically a suffix. is a word that collectively refers to many `` words. (Maybe this could be compared to how the English suffix "-ism" came to mean "doctrine" or "theory" by itself.)
is a made-up word. Without seeing the actual context, my impression of this word is someone who is _jokingly_ keeping distance from someone to see what will happen, knowing they will get together again soon. It's nowhere near "two people saying goodbye to each other".