End of saga: the fault was High Voltage leakage from
the top Backlight to chassis.
It finally dawned on me, that the reason why, with the
Inverter PCB only running and remote from chassis, the
Backlights stayed on. But as soon as you reassembled
everything, you were back where you started. I lost count
how many times I did this. (blame getting old).

Don't be so hard on yourself. This happens to everyone.

The principle is... 90% of the time, all the symptoms needed to properly
diagnose the problem are right there, in front of your eyes, but you don't
recognize the connection. Then when you do, you wonder "How could I have
been so stupid?".