RE: battery charger for smartech skylark
Yes you are correct.
The measured voltage is because the "cheap" wall chargers are not designed to handle much loading, so a small load will cause the voltage to fall lower. Although the measured 13volts does seem a bit high for 9v. I can see 10.5 to 11.5 volts, but 13?
That's probably due to the lower 350 ma that it outputs. That would mean that the transformer(wall charger) has a higher impedance or resistance so a smaller shunt load (in this case the battery) will bring the voltage down.
Hope this helps,
Dan