On single lines with bi-directional services, you can design and implement a token based lock system: it's literally a token, often referred to as tablets, what inspired mutexes in computer science. They are like a golden medal or a durable hunk of metal, with the name of the station it belongs to engraved, often enclosed in a leather case or something. The arriving train drops the token it holds at the station, and obtains the new one when departing. The trains traveling opposite side will return them. When a train fails to obtain it, whether because it merely failed to catch it or the new one hasn't arrived, it MUST stop once, before it technically leaves the part of the rail that is considered "the station", until one is obtained.

This won't work as-is if there's going to be a T shaped crossing in which lines branch from the trunk line into short segments to stations. The crossing must be a station with its own lock token in that case. But that also can be some sort of crude technical stop for staff uses only with just maintenance guys with helmets and vests as station masters and apprentices moving the tokens around.

If they couldn't get computers handle it or make signals turn from red to blue or at least red to nothing, and didn't even have that token system, the train cannot move. It may technically be able to, and maybe it's ok for moving just few meters back and forth, but that's it. The trains should not have been operated at all if they couldn't figure out the computers.

You don't want trains to collide because sick people are forced to work when they shouldn't and realistically can't.

> when it's too cold

You don't want trains to derail due to rails breaking.

> when it's too hot

You don't want trains to derail due to rails buckling.

> when it snows

You don't want trains to go the wrong way (including into another train) due to switches freezing shut.

> when nature drops a leaf on the railroad tracks

You don't want trains to collide as slippery rails made braking impossible.

> or whenever they come up with a new excuse.

Usually it's a reason, not an excuse. Train people like nothing more than seeing the trains ride past, they don't cancel them unless they absolutely have to. Just because you don't personally understand the reasoning behind it, doesn't mean there isn't one.

Try a few weeks of German trains. Sometimes no trains leave on time for weeks.