Hi, I have sold several things for my mom over the years, and I can say that some people are just rude, and there's nothing you can do about it. You have done your part, by shipping the item securely (I assume), and by offering and obtaining a delivery confirmation number. You are not responsible for lost packages via the post office, so I would tell them to take the information to their local Post Office and inquire as to the whereabouts of the package. The mail deliverer has to scan it after it is delivered to the exact address/mailbox, otherwise it will never read "delivered."
I had one person who received a package 3-4 weeks after it was shipped via priority mail. But the shipping updates just said "in transit," and it did not actually say "delivered" until it was ACTUALLY DELIVERED. I would either call their local post office yourself, or tell them to do so (the former if you don't trust them, which I wouldn't). However, I think that eBay might require insurance on all packages now, but I'm not sure = look into that, and see if you're liable even when a DC is provided.
Hope this helps! π Don't let it stress you out. You are not responsible for the USPS.