I confess to being well out of my depth here, Pat, and hope that someone with experience of older Pucks will be able to step in and advise you.

I'm confused by the grey box. Does the battery go in there or is it just where the mains cable enters the caravan? A picture with the cover removed would be useful.

I'd have thought that the two rusty crocodile clips are the connections for the battery terminals. Is there a battery charger already installed - in the grey box perhaps - or are they simply clipped to the battery terminals to power the lights?

Are your caravan lights 12v or mains voltage? Do you have any mains sockets inside the caravan?

It looks like a challenging restoration but one that will give you a lot of pleasure. Be sure to keep us updated on your progress.