Just to revisit this - I actually bought an "automatic setting" clock now that I saw one at Walmart.
Unfortunately, Sharp is lying. "Accu-Set(tm)" is them factory-programming the clock IC and just shipping a button cell in the box and hoping it holds time. My clock was 5 minutes behind and I have to manually set it. No RDS, no radiotime, nothing.
Oi... guess I have to be even more specific in my product hunt.
One of them I bought the feature is not clear if it is 'on/off'. It is a weird tower icon with another weird icon under it. One of them means turn it on. The other means turn it off but leave it on (why). So to make it work you have to have the little tower but the one under it on too. So two toggles to make it work. The other one I bought the thing was supposed to set itself on first power on. Yet to see that work right. Probably have to bring it outside to make work.
You have to specifically look for the feature. Most do not have it.