I don't know how much you're wanting to build and design yourself, or how much you want to buy. But I'll offer an idea which worked very well for me, when I wanted to build a tiny home automation controller that would keep accurate time perpetually without manual resets.
I took a commercially available alarm clock that set itself from our country's radio time service (a WWVB receiving clock made by Oregon Scientific, not that this detail matters) and set it to sound its alarm at a specific time each day. I wrote my home automation software to run on a PIC16F628 microprocessor. These days many hackers would use an arduino of some flavor instead, but it doesn't matter. I altered the clock so that instead of having the alarm signal go to the piezo buzzer, it went to an earphone jack. I took that signal and fed it, via an inverting one transistor amplifier (level converter) to an interrupt pin on the microprocessor. The microprocessor was programmed so that, when it got an interrupt on that pin, it would set its internal clock, and then disable that pin's interrupts for a few minutes.
I implemented a real time clock on the microprocessor, with a timer-based interrupt that was driven by the same crystal oscillator that ran the microprocessor. This was more than adequate to keep accurate time for several days. My requirements for precision were modest, but my goal was simply to eliminate the sort of long term drift that would require me to manually set the clock. So the commercial clock took care of receiving the radio signal and "poking" my microprocessor at the same time each day, thus keeping my microprocessor's internal clock perpetually accurate to within a second or so. This worked for many years until I finally ported my home automation software to run on an internet-connected beagleboard running NTP. It even automatically handled the daylight saving time adjustments in spring and fall.
There are wristwatches available that can handle the receiving details for you. Hack in to one, supply it with power, tap into its alarm output, and you could fit it inside of your own custom made clock.
There are many other options for receiving the time, as well. Many are more elegant. But few are as simple to implement for a one-off hacker's project.