Many years ago, I found this happened to me quite often when I would speak with my grandfather. As a kid/teen/young adult, I would often have difficulties knowing what to say to him. He was rather reserved, "a man of few words" as the expression goes, but he loved to sit and listen to other people, and seemed happy to hear anything and everything they had to say. Since I wasn't good at carrying a conversation all on my own, there were often times where there would be an awkward silence between us. I'd try to find something to say, and would get frustrated with myself when I couldn't do it.
When I was around age 30, only a couple years before my grandfather passed away, I'd call him once every one or two months to see how he was doing. His wife had died over 10 years before then, he was in his mid-80s, and he lived alone. To avoid the awkward-silence problem, I would often get a lined pad of paper out before calling him, and write out a number of topics that I knew my grandfather would find interesting. I remember one where I had about 15 lines worth of ideas, some of which were just single words, which could help me avoid awkward silences and direct the conversation so that I could have a good hour-long phone conversation with him. For example, I knew he liked and followed baseball all his life, so I recall writing "Baseball" on one line, and that became the topic during one of those calls when I sensed an awkward silence could occur.
I'm very glad I have the memories of those phone calls, because it's rare for me to be the one to carry and direct a good conversation
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DSM-5 Diagnosis: Autism Spectrum Disorder, Without accompanying intellectual or language impairment, Level 1.