If you’re on a ship and want to get longitude, you don’t predict local noon. you measure local noon and compare it to a clock that was set to noon at a known longitude (such as Greenwich), and correct the offset using the equation of time.
Even if you ignore this issue and assume you could somehow measure local noon exactly, you still would need almanac data in order to do the correction. Once you are involving almanac data, it stops mattering if local noon has any connection at all to 12:00 on your clock.