Ok, all points you've mentioned are not the case of the problem.
In my car, the key has several positions. If the key is not plugged in, the empeg is off. If I turn the key to position one, the empeg starts playing, engines are still off. In this position I can also use some electrical systems in my car, e.g. the electric windows. If I turn the key further, the engine starts and I get the thump. I think the reason is that car voltage breaks down for a short time and so does the empegs sound output stage. The voltage on the remote line also drops, but it's still enough for the amplifiers to be not muting. When the empegs sound output stage comes back to live the thump is born...