Yes, the lights, as well as the PCB, are powered by the rectified +12 V from the charger, but it only amounts to about half an amp, for what that's worth Do I understand the suggestion correctly that I should power the transistors' collectors directly from the charger, and everything else on the PCB via a diode?
Yes, I think we are on the same page: 12 volts directly from the charger to the lights then a diode from the charger to the circuit with the cap on the circuit side. (anode to the charger)