Ok, I have been able to confirm my suspicion: Indeed, there is a missing link from the GND net of all the components to the GND of the ANT/RIG connectors. Fortunately, there is an easy fix for this:
The recommended solution is a short wire from ANT GND to the rectangular pad of the yellow LED labeled RF1. The picture below shows this modification. Be careful not to shorten the "RIG" GND pin with the RIG signal pin.
One surprising thing with this version of the prototype is the fact that the minimum (all LEDs off) is in the middle of the trimmer potentiometer, not on one end. It may be that the windings on my toroid are a bit sloppy.
But anyway, the indicator works as intended with this modification.
Once the PCBs for the third revision will arrive, I will build another prototype.
73 de Martin, DK3IT