[Carl n Susan]

AFAIK there is NO low-value resistor in the switch. It is a simple on/off switch.

There is no need to ever turn the switch OFF (where you can remove the key) if you are full timing.

Did you measure the voltage after the switch? It should also be 13.4 +/- with the converter running.

The other place to check is the red covered self resetting breaker behind the battery. The left one controls the flow of 12V to/from the battery. They have been known to fail.

The 12V charge circuit is pretty simple. From the converter to the disconnect switch in the convenience center, to the self-resetting circuit breaker to the battery.

All of this assumes you are not getting 13.4 +/- volts at the battery when the converter is running.