I don’t think this actually benefits navigators and astronomers. You just can’t predict local area noon based on clock time without additional data. Even when you have that data, it won’t be accurate to the second anyway.
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.
That doesn't actually work. You can't measure local noon accurately enough for it to give a useful longitude. My celestial navigation textbook estimates the accuracy of this method as 15' under the best possible circumstances, and 40' under more realistic circumstances.
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.
Even if you are at the exact center of the time zone, clock noon is only rarely at solar noon. See https://en.m.wikipedia.org/wiki/Equation_of_time