Need help from auto electrical gurus

[Kevin66]

Why were the parts replaced, solving an issue or just old parts? If they were still working and you still have them i would start putting them back on one at a time starting with the easiest to change first to try to pinpoint the problem.
On another note, just curious what guage the starter cable was.

The car had sat for years outside, exposed to the rains here in the Northwest. Everything under the dash was rusted, so the ignition switched was replaced because of that...and because there was no key for it! The first replacement was a Scott Drake, and the second was a Standard brand. The car started and ran properly for a few weeks with the first one, then began the refusing to stop cranking issue. The second one refused to stop cranking from the get go.
The starter cable is an Accel, and is #2 gauge.

[Falcon67]

Re-reading - I'm with the "bad key switch" crowd.  The I terminal is only there to provide power to the ignition (I) during cranking for cars wired that way.  Some aren't - my Falcon never used the I terminal as built by Ford.  So if a slight turn of the key engages the starter, the trouble IMHO is right there and not elsewhere.  My 1993 F-350 has a replacement key switch and while it cranks properly, getting the key in the exact right position to remove the key and not have the chime sounding is tricky.  It's a regular thing to open the door and have the chime start sounding.  Proper wiggling of the switch housing shuts it up.

[Kevin66]

Re-reading - I'm with the "bad key switch" crowd.  The I terminal is only there to provide power to the ignition (I) during cranking for cars wired that way.  Some aren't - my Falcon never used the I terminal as built by Ford.  So if a slight turn of the key engages the starter, the trouble IMHO is right there and not elsewhere.

Hhhmm? I don't know...yesterday evening we removed the ignition switch. The 3-wire pigtail that presses on over the spade terminals had been replaced too, because at some point it seemed that the 2-wire green/black connector that is fitted over the 'Accessory' post on the switch, had overheated and melted into the original pigtail block some. We removed the butt connectors that spliced the pigtail's 3-wires to the factory wiring, and took it all over to the workbench.

Connecting 12V power to the (battery input) yellow wire, we had power at the red/green 'I' (ignition) wire only with the key over in the 'Run' position, and also in the 'Crank' position. The red/blue 'S' (solenoid) wire had power only while in the 'Crank' position. In my mind, that clears the ignition switch as the cause of the problem.

That was interesting to note, because before removing the ignition switch from the car, we had used a 12V probe light on the 'Accessory' post and some of the wires. When you started to turn the key towards 'Run', there was power immediately in the 'S' and 'I' wires...but no power at the accessory post until the key reached the 'Run' position.

What was also interesting, was that this probe light has a 'red' light for 12V '+' connections, and a 'green' light for use when checking for ground '-' connections. Normally, in order to test for ground, you have to connect the alligator clip on the probe's cable to a 12V source, and touch the point to whatever ground spot you were testing. But in our case, the alligator clip was connected to a chassis ground, and the probe's point was being touched to the 12V source we were investigating. When testing for power on the green/red 'I' wire, as we switched the key back to the 'Off' position, this green 'Ground' light would flash for an instant when the red light shut off. It did not do this when we checked the blue/red 'S' wire, or the accessory post...the red probe light just shut off.

What this momentary green flash means...and what would cause it...I don't know.

[driveamerican]

Check your grounds from block to chassis to body. Just a guess but sometimes things will back feed power if the ground isn't sufficient.

[Kevin66]

Re-reading - I'm with the "bad key switch" crowd..if a slight turn of the key engages the starter, the trouble IMHO is right there and not elsewhere.

RESOLVED...finally!
I'd misinterpreted what my nephew told me when he took the ignition switch over to the bench. I thought he'd said he was getting power only to the red/green 'I' terminal wire when the key was in the 'Run' position, and power to both it and the red/blue 'S' terminal wire when in the 'Crank' position.
That was the case when he tested only the ignition switch terminals, without the ignition pigtail connected. Turns out that when the pigtail was in place, both red/green and red/blue wires were powered, indicating there is a short somewhere inside that molded plug in the 'new' pigtail.
So those of you who said "Just 'cause it's new don't mean it works properly!" were right! Yet another new one is on order. Thanks again to all who gave input, and I will remember this lesson!

[BattlestarGalactic]

Unfortunately in today's world...................Assume NOTHING!!!