I've been wondering about the affix ごっこ when it's a prefix and when it is a suffix. There's the word ごっこ遊び, for example, that means "children's game" or "game of make-believe"; but there's also a song named さよならごっこ that would mean, according some translations, something like "make-believe farewell" or "pretending to say goodbye". But the question is: I think that translating さよならごっこ as "pretending to say goodbye" is purely interpretative because of the context of the song; I say that because it's written in Jisho that ごっこ can also mean "something done together". I, however, have not found even one example that ごっこ has this meaning. Can someone tell me some expressions in that ごっこ has the meaning of "something done together"? If there's any rule about the meaning that ごっこ plays in a phrase, please tell me too.
I think you can forget that definition "something done together". That's simply an over- (or false-) generalization. And ごっこ is basically a suffix. ごっこ遊び is a word that collectively refers to many
○○ごっこ words. (Maybe this could be compared to how the English suffix "-ism" came to mean "doctrine" or "theory" by itself.)
さよならごっこ 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".