a sundial would be far more accurate than a 555anddoes not slip10 30 minutes a month
the time base should be 1part per million error max or 1ppm in a XtalOsc for $1
how about an analog clock with LEDs?
1 secfrom /60
1m from next /60
1 hr from next /12
am/pm from next /2
multiply all these andthatbecomes your timebase
choose32kHz osc or similar to divide to timebase clock.
use Johnson counters (bunch) to drive LEDs directly using R's from each output so second+minute is twice as bright rather than separate LEDs. and hour +minute+second is 30mA. using 12V 300ohm driver from Johnson counters andR=620Ohms to Red LEDs or 560Ohms to Blue or White LEDs
Use smaller R's for minute and then smaller for hour for brighter indication. Choose >=50mA LEDs or increase R ratios. Temporary exceed suggested currents by 50% are ok for 1 sec, but not in direct sun. So further calc for R needed depending on selections of LEDs then buffers are needed for Johnson counters.
-choose SMT reelfor LEDs equally spaced in a circle cutting between LEDs to make arc andusing AWG 30 wire to solder to each isolated cut tracks on reelfor LEDs with a daisy-chained ground for each cathode (-) or use discrete >6000 mcd LEDs.
-cover front with tinted plastic or glass, so only the light is visible and not the wiring. frame with wood, or cosmetic material.
this primitive design will need at least a dozen chips but easy to figure out.use external DC jack for 12V power.
Make it big enough to be visible from outside (water tight) for a long a distance as needed. It can run from solar panel with 12V battery too.