I will share what helped me: My parents were divorced and my father outlived my mother. Not until after my mother's passing unfortunately did I become interested in her family background. This was likely so because she herself was not interested in it, but after her death I received a trunk with old letters and photos she had saved from relatives. I used them to formulate the family history and when I saw my father I would discuss with him aspects of our genealogy. And he contributed his side of the family genealogy as well. I wrote down what he had to say and have saved it. I shared with my father old photographs my mother had and he could often identify where they were taken and who was in them. I used a special photo marking pencil to label them. I also made copies of what he liked and gave him a photo album of them. Would your parents be willing to share old photographs with you?

I found taking a interest in my father's past broke the ice. I learned a lot about past family health history in the process, and that was particularly helpful later to a sibling that was in need of that information. I later regretted not spending more time having my father identify who was in his personal collection of photos. I had only concentrated on his many framed ones.

If either of your parents cook, copying family recipes could be another approach. Other ideas that popped into to mind is I find having a particularly nice flower arrangement present can have a very cheerful effect on the atmosphere. I also recall the many puzzles that the Mayo Clinic had in various stages of completion in their waiting areas. You could get one going in advance with no expectation that they join in with you causally working on it.