767-300,
I agree. The first priority must be to get be ready to follow any RA accurately, and that means both crew, to make sure it is done correctly. Get your finger on the AP disconnect button and think about how much (or little) you are going to pull or push when bitching Betty squawks. Peering out the windows looking for an aeroplane that in a busy piece of sky may well not be the one causing the problem should be secondary.
That said, fellman does raise a valid although probably less-likely scenario.