Should I write to him a second time?

A second message is neither a loss of dignity nor a way to earn an answer. Its usefulness depends on what the first message left open. A practical question with a deadline may warrant a follow-up; another greeting may add little.

If he has asked for no contact, that ends the decision. Otherwise a follow-up can clarify the outstanding point without a stream of new topics designed to draw a response. Your next plans can proceed even if the answer never arrives.