The electronics could be very simple - just count equinox using the alignment of the sun (we don't have a specific date in mind), Stonehenge style.
So charging could be very low current, providing charge is greater than leakage.
Mmm, maybe that is what Stonehenge is? It will pop open soon, spouting confetti....
Or non-electronic, pure mechanical, use rise/fall of groundwater changed by tides to run a clock. Electronics could then be turned on during event day, release chemicals into a battery, and play happy birthday etc. One is only concerned with shelf-life. Bearings etc in the "clock" would only receive two 'ticks' per day, so little wear.