I agree with what you are saying. But the question is, is the “I” terminal connected internally to either of the big posts, in both the ON and OFF states? According to Wells, it is.
The purpose of this whole discussion is to determine if the big posts can be swapped around.
try it. The worse that can happen is the starter coming on when you hook up the positive battery cable.
Yes, the “I” terminal is connected internally to one of the big posts. BUT, it only gets power if the ignition key is turned to start and while the solenoid is activated. In this instance there is continuity between the two large posts and therefore it does not matter which way the current flows through the two large posts.
By “all the time” Mike means that literally, all the time. At least all the time the battery is installed and charged. So that would not be a good thing. There seems to be some ambiguity on that point on how the insides of that gadget are actually configured. It might be the diagram above is a “functional” diagram, not the actual physical connections.
I looked at my truck’s starter solenoid over the weekend, and the I and S terminals are clearly labeled as such, but there is no labeling I could see on the two big posts. And it would be very easy to decide to install it upside down, to make room for something that was getting in the way say, which would swap the two big posts. So I expect @insightful is correct, it doesn’t matter which side is which, big-post wise; and the diagram shown in Mike’s post is a functional one, not the actual schematic.
If you got one of these gadgets in front of you, easy enough to tell one way or the other. With the key “off” and the I terminal disconnected from its wire, measure the resistance between the I terminal and the “starter” terminal. If nearly zero ohms, it’s the way of Mike’s diagram. If not, it’s the way of insightful’s diagram further up this thread. If you value your meter, maybe disconnect the battery ground first