Not familiar with 129.4, but many years ago when I was in the two-way business, there were phone patches designed that could operate on simplex channels.
They had a voice operated relay (VOX) that keyed up the radio from the phone line. Then depending on the equipment, they had logic that after a set amount of time (in setup), would start sampling to see if the mobile was responding. This helped to keep noisy phone lines from keying the transmitter and never dropping. So every few seconds the base transmitter would drop for a few hundred milliseconds, and if it heard signal from the mobile it would pass that audio to the phone line, and prevent the base from keying back up.
When the mobile stopped keying, if the audio was high enough from the phone side it would again key the base transmitter.
So if you were hearing the base station you would hear a drop every few seconds to 'sample' for a response from the mobile.
Depending on how they were connected, it my have been a phone patch operation that used similar logic, rather than a dedicated remote control or console where someone actually pushes a button (PTT) to transmit, and there is no need to 'sample'.