Following my earlier attempts it became clear things weren't quite as clear cut as I had thought. Checking the voltages on the outputs showed that I had made some mistakes with earlier measurements and so there was a negative voltage across one pair. Obviously using the Arduino didn't show that! So time to reconsider my earlier assumptions.
Looking at some more (of the very limited) online documents for the system it does refer to the comm port as being RS-232, which ties in well with the negative voltage I found. I had an RS232 to USB adapter so I just needed to figure out which output goes to which pin.
Assumption #1: GND will be the same as for standard usage and TX and RX will be on the L/R connections.
Assumption #2: The connector is a 3 way stereo version and not one of the more modern 4 way voice enabled versions. This is based on the images I have found online of the supplied cable being a stereo plug and not having the additional connection.
Checking voltages across the outputs give -6.3V between GND and L and virtually no voltage between GND and R (-200mV).
Assumption #3: L is TX, R is RX
Armed with this information I connected to the RS232 adapter as if it were a NULL cable, i.e. TX to RX and RX to TX. Using minicom to open a serial connection to the adapter produced a serial terminal where anything I typed was echoed back. My recollection of serial connections is that this isn't how they normally work...
Of course it could well be that as the controller is meant to connect to a modem then the connections should be straight through and not crossed over? What would my RS232 adapter expect? Swapping the connections over and trying again with minicom gave a terminal where anything I type simply vanished. Turning on local echo would show my typing, but otherwise there was no response. Which feels more like the serial connections I used all those years ago :-)
I have been working on the assumption that the port would normally be active as this would simply the task of adding the external modem or allowing a service engineer to simply connect, but it could be that the controller needs to be told to activate the port somehow? Of course it may be waiting for some particular entry and the baud rate or settings may be incorrect.
Not really sure where I go from here...