You have an amplifier with only one input but you have two audio sources. To change the source you need to change the cable at the amplifier which is uncomfortable (e.g. cable not reachable). You can change the source for the amplifier with a simple switch.
To switch two stereo sources you need only a 2x2 switch.
The connectors you can find in old DVD players, sat-receivers, etc. The switch you can get from different electronic products.
My prototype is not perfectly shielded and only a proof-of-concept. But it works very well. The next step would be to integrate the switch in the amplifier housing.
We'll assume you're ok with this, but you can opt-out if you wish.