The toslink jack connection to the zeppelin air will work only if I'm doing a small pressure with my fingers to the right side (with reference to the back of the zeppelin air)
It is in German and essentially it describes how to open the device to repair a fuse so hopefully it may be of some help. (I couldn't locate any other teardown info or service manual for the device, you may have more luck)
Update (04/28/2018)
Hi,
Does the socket seem "loose" when you try to gently move it from side to side?
If it is soldered correctly there should be no movement.
Looking at the pictures you posted I'm wondering if there is a dry solder joint on one of the connections of the socket.
I can't magnify it enough to see if it is just a spare terminal or whether it should be soldered to a track on the systemboard. It would explain the fact that applying pressure to the right side of the socket would make it work. There may be just enough movement for the connection to be made.
I've highlighted the suspect connection in the image below.
It seems that the socket is loose, so the solution would be to replace this item, but it seems impossible to find it on eBay. I don't even know the part number.