You didn't exactly wait very long... 11 hours is hardly enough time to expect a response, maybe people were asleep, or at work, or out.
In my case I was fixing a radio, then a I went to sleep...
My guess for your requirment would be to make a small relay switching circuit, to replace the push button.
It would be much like a bleep circuit, only it would run off the RX connection not the TX.
Basically you would need to pass 0V from the RX through a diode (banded end towards RX connection), through a resistor (probably about 100 Ohm) to a capacitor (probably about 330uF 16V) and then connects to the 0V side of the relay coil, you would then wire the + side of the relay coil back to the RX as well through a second diode (banded end towards RX), and have a pull up resistor (probably about 2K) connected between the + side of the coil also and 12V supply, then wire the push button wires onto the COMMON and N.O. connections.
When the radio is in RX, both sides of the coil at being fed with 0V (so it is off), when the mic is keyed the RX 0V shunt is removed from the + coil side, so it is then fed with 12V to activate the relay, simultaneously the 0V side of the coil is being supplied 0V by the capacitor, once the capacitor discharges the relay will turn off.
In theory this would work, but it may require a switching transistor to control the relay instead.