The H1542 was certainly first intended to be used with the 553 substation set, but I am sure they must have used 653s with them too. Of course, the reason that the 653 has five wires from the cover to the base, is because in an anti-sidetone set an extra switchhook contact must be provided to remove the telephone circuit from the line completely when on hook. This is analogous to using a four-conductor cord in a 202 telephone set vs. a three-conductor cord in a 102.
But when using the receiver and transmitter of the 553 or 653 to connect to the local intercom circuits (with manager and janitor) the switch box only needs to transfer the three wires from transmitter, from receiver and the common (which was basically connected to the hook switch). So the principle of connections between the 1542 and the 653 do not change.
The person who wrote that description in the TCI document apparently did not quite understand the functioning of the "apartment phone". The description in the first page, does not make any sense. At least not to me.
Why would there be the need for a switchboard ? The phone is a standard local loop substation when in the "central" switch position. When in the other position, it becomes a typical intercom, that's all. The door latch does not provide entrance to the apartment, but opens the front door of the building. When the apartment (or hotel room) occupant want to call the manager or janitor or service desk, they connect the receiver and transmitter elements to the house intercom circuit with the key and push the right button to signal the desired station. When the manager calls, the buzzer sounds, and the occupant also flips the key to the local mode and picks up the call.
I haven't studied the diagrams provided, so I can't make specific recommendations for connections right now, but the principle should be to have the red "handset" wire on the R terminal of the induction coil, and the green wire from the receiver (to GN terminal), and black wire from transmitter transferred to the appropriate posts in the 1542.