I haven't really studied No Train Approaching since the other two have the same thing, but my guess is it comes down to scripting. In MSTS there were two types of signals, the kind that were normally active and always displayed whatever block information existed, and the "nevergreen tree" signals that displayed only red unless there was an active path triggering them awake. In MSTS that was governed by the "Signalnumberclearahead" data in the signal scripts, if the signal script had the "ifEnabled!" statement in the code then it "woke up" as soon as the projected path ahead of the approaching train was within the specified number of signals. After the train passed they "went back to sleep" and displayed red until another projected path advanced to trigger them "awake" again.
My guess is some/most/all Trainz signals have similar scripting so they display red unless there is a train approaching that would need the information. Main trouble is most programmers and game designers were born in the era of CTC, for the last 40 years most mainline signals in the US work exactly that way - signal displays red until a dispatcher or CTC computer activates the signal. If that track isn't being used that day all the signals will be red all day.
As for the AI obeying signals, I've found it does it correctly for the most part, if you have one that stops at a green signal with no obvious reason, select that train, open the message window, and right click the F6 window to give him the "continue schedule" order.
This one isn't moving because I gave him an impossible command, the track to that portal isn't connected. Last night I was testing my latest and started adding wrong way markers to the center express track since the AI kept insisting on crossing to that track - and discovered the reason why they insisted on it, I had the track direction markers on the outer tracks in that section facing the wrong way.
Trainz AI is intelligent but psychotic, drive via makes it less screwy than navigate via, and I've always found that if I order it to drive from Chicago to New York via Hong Kong it will manfully attempt to carry out those instructions until it drowns in the ocean.