It might be that Scobey station I'm thinking of that does not even sign on Sundays. There are no minimum operating hours required on Sundays. If I recall they run 6am to 10pm Monday through Saturday but they are live and local.
In the past, the FM in Sonora, Texas signed off at 7pm, operating 6am to 7pm. Sonora was about 2,500 at the time, in the middle of nowhere and likely barely scraped by at 13 hours a day.
In the 1980s, I noted the Navasota, Texas AM would sign off at, I think, 5:30 even when sunset was past 5:30 and was on, I think 7am to 1pm on Sunday.