Well... Most of the time the auto antenna is powered direct and gets a trigger from the blue 'remote' cable that also turns on all your amps etc. Since there is only one remote cable in such systems, everything turns on or off simultaneously.
However, in some newer HUs there is a separate trigger cable for antenna. This output is only triggered when the tuner is selected as source.
If I remember correctly, I have not seen any budget HUs with a separate antenna trigger output. Still, look behind your HU for a (yellow sometimes) cable marked Antenna.
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