He responded he doesn’t do scheduled time with family and that I need to call him at an impromptu unscheduled time.
Oh, boy, this is exactly the kind of thing my BPD brother would say…
My suggestion is that you don’t take his behavior so personally. He seems to have a issue with not wanting to feeling controlled, and unfortunately there is nothing you can do about this.
If I were in your shoes I would hold a boundary on this. If he happens to call at a convenient time then you of course would answer, and if he is unable to catch you for a couple of months, then you could send him an update via email so that he doesn’t think you’re trying to punish him with the silent treatment. The two of you might even benefit from a lower frequency of contact anyway. My husband only talks to his brother once every 3-6 months, and they are on good terms, so if you are currently talking to your brother more often than that then it might be worth experimenting with cutting back a bit.
But no matter what you do differently, your brother won’t like it and will resist, or turn it into a power struggle. He probably will try to guilt trip you over it, but he doesn’t have to succeed.
Good luck!