I need some information from person A. Person A is not willing to give it to me. So instead of asking directly I keep asking secondary questions hoping that he may say something that might (partially) hint me the information I need. I may even ask other people. Or keep asking so many times that person A would have had it and just told me because he can't stand my questions any more.
It's like extorting, but without using threats or violence, but cunning and perseverance. What word am I looking for?
Although he refused to tell me where he got the money from, I persevered and finally
<???>the information from him.