PIC 7 shows the adapter pluggeg to an AC outlet. The LED indicator shows that its output is active.

I did not include a fuse in my charger but i would recommend one in series with the positive line (in series with the resistor and diode). A 500mA fuse should be good enough. The fuse will give protection when the charger is inadvertently connected in reverse to the car battery. Without the fuse, in my case, the adapter will be damaged. The internal diodes and transformer windings are the weakest link in the circuit.

Good luck DIYing. Post questions if you have any.