I read a long time ago that standardized time zones emerged from the transcontinental US railroad system in (approx.) the late 19th century and a need to create uniformity among times for the purposes of a railroad schedule.

But, prior to that, people were still traveling between time zones. I'm thinking specifically of transatlantic/transpacific passenger vessels, where my understanding is, depending on when we're talking about, it could take several weeks to a month to cross the ocean.

Assuming there's some sort of clock onboard the vessel, how would that be adjusted as they travel into incremental changes in the light? Using the example of a ship sailing from England to America, as they get further west, the sunrise and sunset would start getting later and later to the point where it would be happening at what classic timekeeping would consider midday (if they didn't adjust the clock). Would it occur to them to change it one hour at a time? Or do it in one fell swoop once they got close to America? Would people find it strange for the light to be changing like that? Would the find it strange to change the clock?