Ok, you have elinimated the alternator feedback and the sticking solenoid theories. That is progress!!!!
You now need to check the operation of the ignition switch. They can go out of adjustment with that clunky sector and rack operation.
Open up the column connector. If you have a continuity tester (basically a bulb, battery and two wires) you will want to look at the diagram I posted above and see if the connector (obviously the one that connects to the column and not the other side) gives the same continuity.
The Red wire is the incoming feed. Hook one end up to here. Now probe those wires in Stop, ACCY, On and Start and see what is connected at each stage.
You should have two Red with tracer wires, they will be connected to the Red wire in On and Start but disconnected in Stop and ACCY. If your continuity tester shows they are connected in STOP you have identified the area as being the switch assembly.
Alternatively you could use a 12V test bulb and probe the fuse box to see what is live in Stop, Accy, On and Start. IGNLPS and BUSETBELT are the ones which should mimic the ignition switch and only be live in Run and Start.
BagusJeep lives in Bali.
1981 CJ7 258ci - Bagusjeep
1984 CJ7 258ci - Puthijeep
1981 J20 258ci - Gladys
1951 Willys CJ3A/MB/M38 - Little Willy
1995 Cherokee 4.0 - CHEROKEE