Just one thing that you could check while you are out there that I have seen 1 time. Some systems use the last port to turn on and off the MSG light. You can check the last port to make sure there is dial tone to the port. I remember at least one time that the modular plug needed to be replaced and the system could not turn on the message lights, but would still answer on the other ports.

If the voicemail ports were setup in a hunt group that would also mean that every 4th or 8th call would be RNA, but not if they set the hunting in series. Sine it would be analog you could also use your test set to hear the DTMF tones after you leave a message, if you can figure out which port the system uses to turn on the light.