Contrarily to the abbreviated informal (if not rude) version I used in the title, the usual greeting for the New Year is quite long:
Those are two sentences, and it seems that they are usually pronounced with a slight pause between them. The reply is usually the same sentences:
I am wondering what timing I should use to reply politely.
I have the impression than when communicating in Japan it is seen as more polite and respectful to take time when speaking (making longer greeting sentences), while on the opposite in some occidental cultures it feels more polite to not abuse of the interlocutor's time, and keep communications brief and efficient.
Is it okay to start replying after the first sentence:
Or can I wait until my interlocutor has finished saying their sentence, and take time to say mine too:
And of course Happy New Year everyone!