You have to be pretty ambitious to modify a clock to run for 50 years on a single battery. You also should probably be pretty young if you think you’re going to verify your power estimates, at least ...

If you’re looking for a 1-second time reference, you’d probably just grab a GPS module off the shelf and use the 1PPS output. As demonstrated by [InazumaDenki], though, an old quartz clock module can ...