A 12V solar charger will put out as much as 18V in full sunlight. As stated a solar panel will pull from the battery when it is dark if it doesn't have a blocking diode in it. Most of them but not all will have some rudimentary charge controller. The ones that don't are generally very low output, usually in the mA range. Some systems also have as little as a 4.5V output but the circuit box increases the voltage for the system it is designed for i.e. 12, 24V etc.
As has also been stated you need to ensure you have a good battery and that it starts in a fully charged state. A rested 12V fully charged battery will read 12.6V -13V depending on the battery condition and temperature. Colder temps will give you lower readings. If you check voltage right after you take it off a charger you will get an artificially high reading. Let is sit for several hours and then take a voltage reading. 6V batteries will read 1/2 of the listed values of 12V batteries but the rest of the conditions are the same.
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