Hello! The word "divulge" means to make known private or sensitive information. So it is the act of giving out information. So you could say: "He won't divulge his private information." If you were to use the noun "privacy" then you could say "He won't compromise on his privacy". "Compromise on" means to accept standards that are lower than desired or needed, which, means that his privacy is "vulnerable" to being exposed to other people. I hope that helps!

Divulge means to make known, regarding information, private affairs, etc. So it would be more appropriate to say: He won't divulge his plans. He won't disclose his information. If you want it to be specifically about privacy, I think the word "bother" would be better.