Warning, everything I say below could be completely wrong. It is only what I've hacked together in my head for this screwdriver thing to work by reading existing threads and watching YouTube. If I am wrong here, please someone with actual knowledge correct me.
I think, basically the "screwdriver" method of getting the truck started is aimed at getting power to the starter motor in the event that the motor power contacts in the solenoid go bad. This is only one thing that could be wrong with the "starter" but its probably the most likely thing. If there is something wrong with the little plunger in the solenoid that pushes the spur gear into the flywheel, I don't think the "screwdriver" method will help. Also, if the starter motor itself is bad, your screwed as getting power to it won't matter.
So, what I believe the screwdriver does is get power to the actual starter motor by bypassing the related contacts in the solenoid. The screwdriver is connected to the positive battery terminal with a jumper cable and you touch the tip of the screwdriver to the little piece of bare copper wire that goes between the solenoid and the starter motor. This will cause the starter motor to spin while someone else pushes the start button in the truck which will actuate the solenoid plunger and hopefully start the truck. Note you would want to get the screwdriver in position BEFORE you touch the hot jumper cable to the screwdriver shaft and you need to quickly get the cable off the screwdriver when the engine fires up. The good part here is that the spur gear should retract as normal when the engine fires up.
It would also, theoretically be possible to use a screwdriver to physically jumper the "power in" terminal on the solenoid to the bare copper wire going into the starter motor. If you could position the screwdriver in this position while laying under the truck and then have someone push the start button, it should do the same thing but you wouldn't need the jumper cable. I'm not sure this would be physical practical though.
Here's a pic of what you'd be looking up at while under that truck. You can see the bare wire (arrow pointing to it) but it would be pretty difficult to get the tip on solenoid terminal and across to the bare wire while also avoiding anything else metal.
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