Here you can find a simple, or at least not /extreme micromanaging/ way to set up some sort of vehicle separation.
Guide to Route Vehicle Separation
How to Solve
The simplest way that requires literally no management at all would be to have a two-tracked route that is only used for one line, has no level crossings and runs 24/7. Then just put down trains at roughly even intervals and unpause the game. The issue with this is mainly that it’s only cost-efficient when using lots of trains on lines with decent ridership even in the night.
The optimal way is using the Departure Time setting to stagger your trains. This is also pretty much necessary if you want to have shared sections of track.
The best way is to manualy set departure times.
Every train start and end their route at either the same station at diffrent times, or diffrent stations at the same time, will keep them more or less synchronized. You can exploit the off map stations in this manner because they have an unlimited platform capacity.
For example, on the first map you can double track running all the way from north to south and assign each train to one of the two off map stations, and then set them to depart from that station at 8. This means every morning both trains will enter the map full of rush hour commuters, on opposite ends.
This puts two trains leaving at peak hours with maximum possible separation. Once they pass each other, they will eventually reach the other city and turn around. The whole round trip takes a few hours and you can even make them do another loop in the other half of the day, but you might want to fine tune it to avoid running during a dead hour when there are few passengers.
From then, it’s just a matter of adding more trains into more timeslots that won’t conflict.