I had not been able to make more progress on this topic until today. I did some electrical measurements but found unexpected results. Which made me stop and crosscheck with the community here. I'm not sure if everything is as it is supposed to be, or that there's something wrong.
(*) At first I measured the voltage on the connectors at the sender unit. I expected to measure a stable voltage, but it wasn't stable. It was fluctuating between zero and about 4~5 Volts. All kind of random values appeared on my multi meter. Unfortunately do I not have an oscilloscope to see what's going on.
(*) I then disconnected the cable that connects the sender unit to the gauge. When this cable is floating the gauge indicates below E (empty). When I short circuit the connector to ground the gauge indicates more than F (full). This is what I would expect, no surprises here. With the connector off was I able to measure the resistance of the sender unit. With the current fuel level is it about 42 Ohms.
(*) However, when measuring the open voltage on the cable I see again all kind of random values, fluctuating between zero and about 10 V. When I short circuit this wire to ground via a current meter I see that it is switching between zero and 0.29 Amp. Almost in a 1 second on, 1 second off manner.
So my question is: is it normal for the voltage stabilizer in the dashboard to show this kind of on/off switching behavior?