I might have the answer. It seems the dry contact can be used to ring the doorbell.
I just read through the document for which I provided a link in Post 4. This sentence from near the end of the installation instructions of any help:
The 24 volt/2Amp dry contact switch closure may also be used for home automation or security panel panic alarm interface.
Just in case this is not clear, "24 Volt/2 Amp switch" doesn't mean there's 24 volts anywhere in the system. It means this switch is rated to switch up to 24 volts at a maximum current of 2 Amps.
The ordinary non-lit doorbell button is a dry contact. Doesn't that mean you can use this unit's dry contact so that pushing the intercom button rings the doorbell? As I said, the instructions aren't clear enough to think things through... is that dry contact a part of the intercom push button, or is it a separate switch?
