It's not a terrible thing to have your amp on, with ignition on. It draws very little current, and doesn't affect the life of the amp. It's just a non-ideal config.
You could try to tap into the antenna, I assume it's a powered on(amplified antenna).
Otherwise, it's normal for an amp to be on, even if a headunit is off. As an example, my bluetooth and street guidance wouldn't work otherwise...
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2012 X5 xDrive35i Sport Activity - Alpine White - M Sport Package
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