I had no luck trying to find etymology.

That's because its is a troubled one. From Latin reciproco 'to move backwards, or back and forth'. The re- prefix is familar, but the rest of the word is murky. Cf. Latin procer 'chief, noble'. But where did the -ci- come from? Some kind of strange reduplication? Anyway, re for 'back' and pro for 'forth' is about it.