To be honest, I don't have access to the book right now nor can I remember if it sheds any light.
It sheds a little. The meeting directly after Vito's funeral includes, "...Tom Hagen forsaking his strictly legal role to rally around in this crisis...", then he stays on after everyone else has been dismissed and he and Mike assess the situation. From that point on, he seems to be functioning as consigliere again.
