If you can afford an atomic clock then I guess that answers my question about "What is your budget?" - $Thousands! But seriously: what sort of money are you wanting to spend?
You still have not said how accurate the pulse needs to be: can you withstand the pulse being +/- 1nS or +/- 1uS or +/- 1mS? I'm sorry by 'pretty accurate' is a very hard to match engineering requirement.
Also you have not said anything about drift: if you will allow +1mS out, then that can mean up to 1 second out after a bit over 16 minutes - if that acceptable? Even at +1uS, that is 1 second in 11.6 days.
What external sources do you have available? For example, can this device have an internet connection - if it can then you could reset the clock every so often using the NTP.
Susan