Missed the testing with out the battery the way you wrote it is a little confusing. so you still need to test the converter with no loads on the converter at all, so that doesn't mean just unhooking the battery cables as you have seen you can still run 12V with out the batteries. basically unhooking the output of the converter and testing directly.
here is how you test it from the manual
TEST. First, disconnect all loads and battery on the Converter/Charger by removing all 12 VDC connections from + or POS . Second,
attach a multimeter instrument between the positive and negative terminals of the Converter/Charger. Then energize the 120 VAC converter
circuit. Test for proper output power using the multimeter. Measure the output voltage from the positive and negative terminals. The voltage
should read 14.6 +/- 0.2 VDC. Add 12 VDC load connections to about 2/3 of the rated capacity of the converter. Recheck the voltage, which
should remain approximately the same as at no load. NOTE: If the chargers output voltage is set below the battery voltage the charge will
not charge plus the LED will not come on.