Well, I'm female, but I too wanted to feel closer with my Dad who was also pretty closed mouthed. I loved him dearly but felt like there was something missing.

So I'd sit and ask him to tell me about his Mom & Dad and what they did when my Dad was a kid. Then I'd ask Dad about when he was in school -- see my Dad got "asked" not to return to school when he was in 4th grade cause they said he was a distraction -- he had Tourettes' Syndrome. So he never got past 4th grade, but he taught himself Math, Trigonometry, Calculus, and all about electricity so he became the head electrician at Corning Glass works at the plant they had in our hometown. So I was extremely proud of my Dad. In fact, when he was 17, which would have been in 1932, he broadcast images of people across town - in other words, he made the first TV set in our area (who knows, maybe anywhere!). So I had ALOT of material to ask my Dad about.

You have to know alot of background info in order to ask your Dad about stuff. I got all my info from my Mom -- who got HER info from my Dad's mother. His Mom was dead before I was born, so I couldn't ask her.
But ask your Mom to give you as much info as you can about your Dad, and go from there. Pick her brain -- she should be able to help. If he was in the service, ask him about that! That should be good for a lot of questions & conversation.

Just a suggestion. Hope it helps. Take care. Hugs, Lee