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Why would a 12v panel put out 18v?

Not to me. Once you connected them in series, it should be 24v. We need an expert here, I get a headache.

But there is clearly something more to it, if you test the panel and it shows 12v (or more likely something in the 13s). But I don't see how, from that diagram.
Easiest to demonstrate with a couple of AA batteries. You get 1.5V from each. The only way to get 3V is to touch the narrow end of one to the wide end of the other AND measure across BOTH of them. If you only measure one battery, you will get 1.5V, regardless of whether it is touching another battery or not.
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