First, the variations in the voltage coming from the panels was due to a faulty volt meter (I should have never gone with the Fisher-Price model).
Once I started using a real volt meter, the actual voltage on the leads from the solar panels, whether connected or disconnected from the controller, are a consistent 24 volts in bright daylight.
I can’t figure out from the attached schematic, or anywhere else, whether this output voltage should be 12 volts, or 24 volts (i.e: in series or parallel).
The schematic appears to show four solar panels, but might only be two sections of two panels, by the way they’re wired.
Still confused.