My air conditioner sparks, but only sometimes, even with a new cable
Now it's a week later and since an hour I have a new air-con installed.

The technician from the old air-con was here basically every day last week. And every day he fixed some more cables and every day it seemed to work when he left. Most of the time it worked for at least an hour and then not anymore.

Finally, since last Friday we didn't have any sparks anymore. The air-con started ok but then after anywhere between 10 to 30 minutes, it was not cold anymore.
Finally, on Monday, the air-con guy diagnosed that the compressor sized and it's time for a new one.

This is obviously not "the" answer for every case like this. But I wanted to let you know that this is what happened in my case. Maybe this will be helpful to someone else in the future.