If it were me, I'd be thankful that T accepted and responded to my email and resume what we've agreed on - one email a week.

I wouldn't start pushing boundaries about something that has already been agreed upon. If it was really important to email more, then that is something that needs to be discussed face to face in a session.

The whole keep-emailing-because-he-gave-in-once seems rude and inconsiderate. JMHO.