Contacting a potential research adviser
If you think you are on the edge of being annoying, then it might be better to wait. But, you don't have to wait passively. See what other, backup options you might have with other professors and start a conversation there. Be a bit tentative with them, of course. 

And, if he is negligent about responding, note that he might also be negligent about giving you the guidance you need. So, other options are worth a look. 

But, it is also possible that he is just a last-minute procrastinator sort of person, so be prepared to spring into action if you get a favorable response.