This circuit is the solution for you!
It is pretty similar to another project I posted a while ago, but here it turns amplifier on and off. If source is playing then the unit will turn amplifier on by using the sending the remote infrared code to turn it on, and when idle for some time, the unit will send the power off remote infrared code to turn off the amplifier. The code here is set to work with a Kenwood 6030 amplifier. If you have a different gear, no fear. Changing the program to work with another set of codes is really simple. You will need to change one or two hex codes only in the KenwoodIdle.PDE file. The best place to learn the codes of your gear is by looking at http://www.lirc.org/
The PCB shown in the picture is part of a shield designed for similar idea that also includes Equalizer bar-graph of the music. The circuit here is a subset of it and for it no PCB is really necessary (but since I got 10 PCBs in a batch... I got some spare ones).
Step 1: Parts & Assembly
1x RGB LED (optional)1
1x 330 Ohm Resistor (220 to 470 good as well)2
1x 220 Ohm Resistor (100 Ohm is even better for the IR LED)3
1x IR LED (most likely you need 940nm one)
2x 3.5mm Stereo jacks
4x 22KOhm Resistors (10K is minimum, 56K is maximum I believe)
You will need Arduino IDE 0022 as I did not see the IR Remote library ported to the Arduino 1.x IDE yet.
Put the files in IRremote sub-directory into the Arduino libraries folder
Compile and load the program to your Arduino.
1) Status LED is optional, you don't really need it. but it is useful:
If showing Green, that means amplifier is ON but no music is played by source
If showing Blue, that means amplifier is ON and music is played by source.
2) Increasing the value of the resistor of the status LED will make it dimmed which might be desired. I use only one resistor and that means that you can only have one color at a time from this RGB LED. In this case it is by design. If you want to play around with different colors and stuff, you will need to move to three different resistors one for every color. Note that if you do that, the resistors should be slightly different between the Red, Green and Blue ones (for example 330 for Red, 300 for Green and 270 for Blue for the RGB LED that I have).
3) Reducing the value of the resistor of the IR LED can increase the distance between the IR LED and the amplifier under control. Do not go below 100 ohm otherwise you might fry your Arduino. I used 220 Ohm as I placed the IR LED very close to the amplifier IR sensor.
How to connect to your Stereo system:
The amplifier output should be connected to an output of the amplifier, connection to tape recorder is typically not used anymore these days and can very well be the best place to connect this unit to your amplifier (recording output of tape from Amplifier to the Amplifier jack of this unit).
The source input, marked as Sonos in the diagram below (this is almost always the source of music in my house these days) can be taken from RCA connection of the Sonos or using a split cable take one into this unit and the other to the amplifier.
Enjoy the listening.