Getting back to the original question, I seem to remember that at the time and place of the robbery the re-signalling for the West Coast electrification was in progress but not yet complete. The absolute block signalling still in use at the time might have had track circuits in some places, that would illuminate a light on the signalman's panel if any part of the train was within a track circuit. But the line was not continuously track circuited so in general the signalman wouldn't know where the train was unless within sight of the signal box, and wouldn't necessarily know it was divided unless the front portion passed the signal box with no tail lamp on the rear.
The re-signalling provided continuous track circuiting, so the signalman would have know if the train had moved between sections which would typically be about 600 yards long. There would still be no indication of what the train was doing when within one of those sections.
There are some signal box diagrams online that would give more details of the signalling. If anyone can remember the name of the boxes then a search might find something.
I am awaiting some information (if I can get it !) , on the absolute block signalling on the route , before the commissioning of the Bletchley Power Box (which controlled south of Tring to north of Hanslope Junction / north of MK in the real world , not the railway world !)
Sears Crossing was the box in question , and it may have had some basic track circuits (an indicator , not neccessarily a "red light" in the box)
One assumes the Up Postal would have been offered forward to S Xing from the north , accepted under the block instructions , train entering section given and "offered" forward to the next box (Tring ?) - standard signalling procedures.
If the train had not arrived - the controlling signalmen should have implemented the standard rule of "train unusually long time in section" , which means that another train wold have been stopped , cautioned to proceed slowly on another line , and report back if anything amiss was spotted (like a broken down train , or even a mail train robbery) - the nearest Station Master and Operations Supervisor wold have been called out for an incident like this , and they would not have been that far away - at the furthest Bletchley , though there was then an SM at Hemel.
If the communications and phone lines were cut , then another set of rules should have been applied , basically proceed ahead , at a very slow speed and look out for "trouble" / report back at the next open box. (or manned station) .
There ought to have been other trains around , in fact I am anecdotally told there was a goods train that passed the robbery.
There would of course be a very full internal railway enquiry into this , the question is , have the files been archived or destroyed. (or withheld due to extreme sensitivity) - they MIGHT be in Kew.