How to organize the inclusion of an external amplifier?

Question

Do it yourself

Briefly: it is necessary to organize the switching on and off of the external audio amplifier by turning on the signal source.
There are radio clocks. Cheap, no line out. The sound is appropriate. I thought about bringing the signal to large speakers. There are speakers, the amplifier ordered from the Chinese. The issue is power management.
The idea is to automatically power the amp when the clock radio is turned on. It consumes 12V, a relay can be built into the circuit. The only question is where to get the power control signal from.
The situation is aggravated by the fact that you want to interfere in the design of the radio clock minimally. The case will have to be opened in order to screw in a 3.5 mm jack to remove a stereo signal. But I would not want a lot of extra wires, since the clock radio will be in plain sight. Ideally, to determine the fact that the clock radio is turned on by the presence of some potential on the signal wire (ie, on the stereo cable that goes to the amplifier). Is it real at all?
PS An additional question for the "five" :) - where is it better to shoot the stereo signal itself? From the output to the regular speakers of the radio clock, or is it better to dig deeper into the circuit, to find an "honest" linear output? The first is simpler, but IMHO the sound quality passed through two Chinese amplifiers in a row will be below the baseboard. The second option is better in terms of sound, but then, most likely, it will not be possible to adjust the volume of the system using the standard clock radio buttons, because. usually the final amplifier controls the volume...

Answer 1

If anyone is interested. Between the signal (left or right channel) and the common wire at the output when the device is turned off (standby mode, the clock is running), 0.6 millivolts were found. When the device is turned on (ipod mode, paused, i.e. no sound) - 4-5 millivolts. Theoretically, it is possible to build a key on this gap, but the rake crept up from the other side.
During the test assembly of the system (receiver + external amplifier), a wild background was found in standby mode. Well, to the heap - the amplifier gives out wild interference, which completely jams the radio reception. So I'll try to screen it, but if it doesn't work, I'll close the project as insolvent...