My goal is to alternately get into his line of business. How do I make it clear and utilize his support?
Did you try asking him point blank when you had lunch with him? If you don't say anything,he doesn't know anything about you. If you don't ask anything, you won't know anything. If you don't ask for anything, you won't get anything.
After the lunch we decided we will meet again in three months to catch up.
I don't know what the two of you are up to,but this is not my idea of mentoring in real time. Are the two of you making any effort to keep in touch within those three months? The whole point of having a mentor is to be able to get some ideas from the mentor, get some feedback from the mentor in a timely way if not in real time. Unless you are moving toward your goals at a real stately pace, that is. Frankly, I see contacting such a key person as a mentor every three months as a joke on the concept of mentoring. If it's not fast paced,if it's not intensive,if it's not aggressive and it's not in real time, then the mentoring is not all that credible. The two of us need to rub your energies on each other, and move with the aggressiveness of an armor unit, the audacity of a parachute unit and the terminal effectiveness of a commando unit. If I were your mentor, you'd have my cell number. And I'd have yours. And you could call me or leave me a voice mail 7x24.
... what else should I do to engage him so he knows more about me and build trust?
You engage him by bouncing ideas off him and asking him for his feedback in real time. You keep him apprised of your progress and you are not shy about asking him for advice. And if you don't happen to like his advice, you ask him what assumptions and presumptions he made when he gave the advice. Learning how to look at things in different ways and from different angles is no small thing.
You don't have the answers, so at least, you need to show that you are asking sharp, searching, no nonsense questions. If you want the right kind of answers, you have to know the right questions to ask. On occasion,I have asked questions that totally motivated the answer provider to want me to be at their side, backing them up.
If you know how to ask the right questions, you can become your mentor's sanity check and sounding board. There will be times when you will be valuable to your mentor both because of your ignorance and because of your ability, starting from a zero baseline of knowledge, to work out sound and credible answers.