If you do what you said you were going to do, and nobody notices, does that still make you responsible?
Only the responsible ones know how to properly answer that question.
There is no picking and choosing. There is no waiting and hiding. It’s not a social activity. You are either responsible, or you’re not.
But you can usually tell the ones who are responsible all the time from the ones who are selectively responsible (i.e. only do things when people are around). They are the ones who ship things. They are in the right place at the right time doing the right thing. They take initiative. They start. They finish. They do things that matter without being told.