You should have a disconnect somewhere May say USE/STORE or AUX on/off
Also you should have a circuit breaker or fuse in line. Likely close to the battery but mine was about 15 feet down the power road.
also there are fuses on teh converter.
Question... Do the lights get brighter when you plug in? (Converter is working)
Next question You said 10 volts. 1.414 times 10 is 14.14 I point this out because if the meter is set wrong you may be showing 70.7% of the voltage (The inverse of the square root of 2 times the voltage) has to do with the meaning of RMS on some meters. (Some meters if set to AC read the peak and multiply by .707, others read the true RMS and are not so affected).
I have both kinds.