It could well be a fault on the Car/caravan 3position switch. ie:car/caravan/towing centre being the correct setting for towing.
Indicator light shows current going to the switch but not coming through switch to feed 12v system. Of course this assumes ithe switch is not jammed in the mid postion which powers fridge via tow cable.
I think the switch is a push fit pull it out and test the 'out going wires with a multimeter or a circuit tester for cars(best one is the steel with screw cap over the spike.)
What you could do if you have bypassed the charger, econnect through the charger as it was and see if all 12v system works if so the go by that leave the charger in the ciruit a look for another charger through caravan breakers.
I think the confused bob did not read the car caravan switch bit of your question. Failing that look for a disconnecte wire which may be the cause.
from another Bob
May 2013