You kind of thru me off with "not even a click". That phrase is used when a person has an electric solenoid starter where you rotate the key to a start position momentarily and then let go when it starts. Like all your newer vehicles. The "no click" means the solenoid is not even trying to cycle.
In your case there is a foot pedal that operates linkage that slides a gear into the flywheel gear and at the same time pushes a button on top of the starter to make the starter spin. So even if the battery is dead you will have lots of "clicks".
So open the hood and look at all that mechanism. Have someone push on the pedal with the key off so you can see how it all works. Observe if the gear is sliding toward the flywheel and observe of a lever pushes on a big button on top of the starter.
I guess you are saying that your truck battery is always on a trickle charger. Is that right? So I guess it will show 12.6V when you check it. So if it does and the battery is not "breaking down" the instant you push the pedal, and when you observe under the hood, the big button gets fully pushed, then we know it's either that big button switch or the starter or cables or ground.
So now you know what you are looking for. You know you have to familiarize yourself with how it all works so you can catch something that does not look right. Be careful and be sure truck is in neutral with Ebrake on. Even with key off, the motor can start for a split second. Truck would lurch if not in neutral.
So we are now trying to find out if battery has 12.6V, if button on starter gets pushed and if starter spins. Let's don't use the words "not even a click". Let's describe what is or is not happening under the hood.
Also be advised that all we have to work with is what we can learn from you. You have been skipping a few questions. I need them all answered or I wouldn't ask. Go back and read the post and be sure you have answered every question. Without these answers you are shutting down your own post.
Take battery OFF charger before measuring. Report both measurements as described. Posts/clamps. Don't do anything or replace anything without telling us.
