There are special controllers within the system that handle this. These same controllers also handle the automatic station identification (CW ID).
The voted audio output is routed into this controller, and from there, to the dispatch console and to the transmitter. The audio routed to the dispatcher is normal voted audio, the audio routed to the transmitter is the "busy tone". When the controller detects a console transmission ("console priority"), that audio is routed directly out over the air.
When the unit calls for "the patch", the dispatcher can then press a key on the keyboard to enable this operation which sends a signal to the controller to route the voted audio out over the air instead of the busy tone.
In the event of a loss of connection to the dispatch equipment, the system operates in a fall-back mode, often referred to as "self dispatch". In this mode, the busy tone is disabled, voted audio is routed directly to the transmitter (simulcast controller, actually), and the "repeat" function essentially is the result. The individual sheriffs stations will then dispatch calls over the air using control stations talking into the repeaters just like a mobile or portable.
It's not perfect. There are occasionally little glitches where "the patch" will be up, but you'll still hear a blip of busy tone just before the unit audio is heard. It is a TRULY one of a kind, custom-designed system.
I'm sure someone closer to the system can be more specific, but this *IS* how it works.
Oh, and a few little-known facts: The audio deviation is actually lower than they are authorized for because SUPPOSEDLY back then, GE couldn't get it to work properly without the deviation level being around 3.something kilohertz. Same deal with the transmit PL tone - LASD mobiles and portables are SUPPOSEDLY carrier squelch receive, and no PL is transmitted because GE never figured out how to get it to work.
The RF hardware is GE MASTR II vintage, with GE MASTR II transmitters and receivers, MASTR II auxiliary receivers, MASTR series voting comparators, and all kinds of custom equipment such as simulcast controllers, audio controllers, GE STAR and MDC 1200 decoders, etc.
Talk about a mess. The guys maintaining it must make a fortune as there likely isn't anyone else who knows enough about it to keep it working.