Unless you are doing a museum quality restoration, I would recommend changing the battery location to either the tongue in a box or inside if you use AGM batteries. Use the original outside box for storage if you want to leave it in place.
The reason is that although the long narrow battery which was used in those boxes is available (with difficulty in locating one) you will almost never find one which is deep cycle, and you want a deep cycle battery in your trailer, not a starting battery.
I think but am not sure, that those funny narrow batteries may be still available at places like Tractor Supply and other farm store type locations, as they were used in old 12 volt
tractors, which last forever, thus the need for those batteries.