>For just three signal aspects, this can be done through the rails without line wires.

Across the Suisun marshes, the SP had 4-aspect signalling using polar track circuits -- not sure how they arranged the 4th indication.

> signal to display a hard yellow approach

What does a soft yellow look like?

>ABS for single track gets far more complicated, and does require the use of line wires. Here is where things get confusing. A train that passes the head block signal (leaving signal of a siding) will cause all the opposing signals to "tumble down" up to the next siding and give a red signal to any opposing movements.

Yes, this is the essence of GRS's AP-B system. After you study the circuitry, it's not at all confusing. I looked for a link to GRS-135, but no one has made a pdf out of it and posted it yet.

>If the circuits do not allow following trains,

The whole point of the AP-B system is to allow for closer following movements than opposing ones. The GRS booklet specifically makes this point as an operational and economic consideration. GRS designed th system and named it. Since then every one else, including the ARR's Signal Section, has copied the basic principles (demand operation, overlaps at sidings, and the directional stick relay).

>If all the signals are at least three aspect and can display a hard yellow approach, then the circuits will usually allow a following train.

There are plenty of cases on the SP where only two aspect signals were used for this very purpose. As we discuss this, the CORP is the process of removing the last of them from the Siskyou line between Black Butte and Springfield Jct.

>Now, if you simply remove the number plate or add an "A" plate to the head block signals, you now have an Absolute Permissive Block system (using the signal definition, not railroad).

The photographs in GRS-135 show Monon and NP trains passing signals at ends of sidings, and the signals have number plates. This business of adding A plates is a latter day thing (probably post-dates dates WWII), and the removal of number plates dates from the 1990s.

>If there is only one intermediate signal between sidings, then they have to be a staggered pair or have overlaps in the unlikely event two opposing trains enter the block at the same time meeting unexpectedly at a red signal.

The overlaps would be in advance of the leaving points of the sidings, not in between. There is no reason to stagger intermediates simply because there is only one set between sidings.

>I have absolutely no idea how the modern signal systems work that use an electronic signal through the rails between signals

Sometimes not very well, particularly if there has been nighttime crop dusting and few trains running.

Let's try not to conflate transit signalling with RR signalling, while there may be similarities, they're different types of operations dancing to a different set of rules and regs. Remember the WAMTA collision(s)? Different type of track circuits, not to mention the signal control.