Newer FoMoCo products indeed have a solenoid mounted on the starter that moves the Bendix gear into position at the flywheel. It takes the place of the internal 'shoe' type mechanism. The shoe acted as a solenoid, using the starter field winding, or part of it actually, to act as an electromagnet to pull the shoe into position, thus making the winding more effective [having an armature instead of 'air' ...], and moving the Bendix.
The roundish item near the battery was always called the starter solenoid by Ford owners as the 'follow-thru' starter of old had a Bendix drive that was shoved into the backside of the flywheel by the rotation of the starter motor armature. Some 'backward' spiral grooves made the spinning of the armature shove the gear towards the flywheel teeth. Thus, there was no 'starter solenoid' needed to move the gears. Ford has finally gone to the old GM design with separate solenoid, etc.
Likely has something to do with needing smaller motors with larger torque capacity. And, newer starter motors have permanent magnet fields, rather than generating fields by using electromagnetism. Things change...
tom

 

Interesting. But, how do I perform the jumper test? Do I disconnect the + cable? Do I need a certain gauge of wire or some sort of kit? Do I disconnect wires from the relay or solenoid first?

 

You never got the question about how to jumper answered... sorry.
To test the 'switch' near the battery, you could use a screwdriver blade. Touch the post connected directly to the battery positive with one end of the screwdriver, and keeping contact, touch further down the blade to the small lug protruding from the solenoid body. {You will get some small sparks.} That will supply juice to the windings of the solenoid, and connect the large posts internally, and energize the starter. Do this with the vehicle ignition disabled[off], and the truck in neutral or Park if an automatic unless you want to start the engine.
When you move the screwdriver from either the battery size post or the small post, the solenoid should disengage, and the starter should stop. The only way the starter can run on after you release the key is for the solenoid to stay engaged somehow, and there is no way for that to happen unless 1)the solenoid is gummed up, or 2) your ignition switch is sticking, and keeping the solenoid engaged. The above will test the solenoid. You can be sure the switch is not causing the problem by removing the small lead from the solenoid when the problem occurs. If the starter continues to run, the solenoid is stuck in the 'engaged' position.
tom

 

Ok, here's what I did. I have a long enough crescent wrench and used it to jump the + battery terminal to the + lug on the solenoid (yes, I was wearing a glove). The starter energized and then stopped when I disengaged the jump. I did this a few times. On the third try the starter remained engaged for a few seconds. I disconnected the positive (red) connector from the solenoid and tried again and this time the starter remained engaged for about 5 seconds. If I'm understanding your previous post correctly this indicates the solenoid is sticking open. Does this indicate a problem with the solenoid near the battery or the one attached to the starter? Thanks.

 

Which + terminal on the solenoid? The large terminal where the wire directly to the starter is bolted in place? The small + terminal that energizes the solenoid?
Which positive (red) connector did you disconnect? Yah gotta be more specific.

If the starter stays engaged with ANY of the large red cabled disconnected from the solenoid near the battery, you have a mechanical problem in the starter. Likely it is gummed up or needs lubrication & cleaning. If the SMALL wire is disconnected from the solenoid near the battery, and the starter stays engaged and running, the solenoid may be staying in the 'engaged' position, and thus connecting the large + wire from the battery side to the large + wire leading to the starter itself.
tom

 

I jumped the + battery terminal to the large + on the solenoid then tried it jumping to the large + on the solenoid with the small + (red) wire detached.

 

Which large +? To energize the starter there are two ways involving the solenoid on the fender. 1)jumper from the battery + to the SMALL solenoid connector. The starter should turn. If the starter stays turning after you remove the jumper, the solenoid must be sticking IF the starter continues to turn the crankshaft.
2)You can BYPASS the solenoid on the fender by using a jumper cable from the + on the battery to the terminal on the solenoid that connects directly to the starter. YOU WILL GET SPARKS. In this case, if the starter stays engaged after you remove the connection, it is a mechanical problem with the starter motor. The only way you would know is if the engine starts, and the starter keeps turning. There should be no other way, as there is no power to the starter motor after you remove the large jumper.
As much time as it takes to explain all this, you could have replaced the solenoid 10 times, and would have known if it was sticky, worn out or not. Just replace the solenoid on the fender. It must be giving power to the starter for it to stay running.

tom

 

I think I will try that. This thread seems to have gotten into some deep weeds. Just for the sake of clarity, on the fender solenoid there are two large terminals. One is attached to a red cable the other to a black cable. There is also a small terminal connected to a small red lead. I was jumping to the large terminal with the red cable. Since its only about $20 I'll just replace it and see what happens. I still think its weird that it only happens after multiple starts. Thanks.