Here is possibilities for not shutting off.
Somehow the coil is being fed voltage.
Something hot is tied into the wiring for the coil.
Solenoid is not wired right.
The ignition switch may need to slide a bit forward or rearward.
Trace out the resistance wire ("I" wire also) see if someone tied something extra onto them. It should look like the diagram.
First two diagrams are the solenoid. Third is bumping (the reason my stuff is opposite from original. The big posts do not care which side the starter cable is on. As long as the starter cable is by itself on the chosen post. I wire mine as in my pictures (backwards from original). For me, this will allow me to bump or start the Jeep with a screwdriver from the battery cable side against the "S" terminal. The original way will not allow the screwdriver to reach "S".
I have a diagram for a 1979, it is probably about the same for an 1980 and 1981.
I am going to send several diagrams. Keep in mind I had to color all of the wires in "Microsoft paint" from two pages scanned from a manual. I did this years ago. Colored markers used in a manual with lines close together just never did cut it when following wires!
Solid colors are correct. White wires show up black. Along the wires somewhere it is written the color.
Note: Wires with stripes or color tracers are colored with the correct "main" color. The diagram did not denote what the color of the stripe was. I made "dashes" on these wires just to let you know it does have a tracer stripe-color unknown. You will see this. You will get used to it.
In these diagrams, the 304 is shown top left. However, it shares the rest of the wiring with the 258 six cylinder (Like I have).
I "rob" parts of the diagrams to explain things, you will see this with my ignition diagram.
I had the office store blow up my two pieces, I mated them (they overlap) and had the whole deal laminated. About $25.00, it was well worth it in tracing things out.
I can maybe slow down some, I will be happy to try to explain better. I am here just as long as it takes to get you squared away. Some go on for months! CJs are my cup of tea!
Images (Click to enlarge)
Thursday, October 4th, 2018 AT 7:21 PM