Hi Amanda,
Many people talk about the "Earth" on a 12 volt car or caravan system, but they don't mean that really - they mean the electrical return path to the battery.
And on a 12 volt system - there's loads of places that corrosion or loose connections can rob the system of power and reduce the voltage across the bulbs.
The corrosion or loose connection can be in the live feed or the return. But if all your lights are equally "dim", then because the return is shared, that would affect all the lights equally and would seem to be the cause of your problem.
Trace the return wiring back to the caravan connector, clean and check each connector you find on the way - if they are push-fit connectors, pull back and brush clean (old toothbrush might work for you) and protect with a smear of vaseline - other connectors may need a spanner to undo.
But the important thing is to make sure the connectors make good metal to metal contact - and that there's no a layer of gunge between.
Lastly, don't forget the return feed in the 12N caravan plug and car socket - these are exposed to the worst of the weather and easily crud up - especially inside the plug and socket if the rubber boot is a bit loose.
Robert