Anderson Plugs

Heaps of stuff you need to say before anyone can help.

What size and type of battery is in the van.

What size wire and connector type is used from the tow vehicle to the van battery.

Most original installations in Tow vehicles use wire that is too small and the connections between the van and the tow vehicle are not heavy enough to carry enough current to charge the van battery correctly and fully.

Alot of variables with your question being size/type of the battery, alternator & cabling & exactly how much draw the lights & TV will use.
As an example if you ran 16mm leads through the Anderson plug to a 100ah AGM battery in the van, it would take a modern car around an hour of driving to charge it from 30% to 90%. It may take a further 2 hours to get it near full charge.
Charging at idle is less efficient although leaving to run for an hour may very well replace the small amount of power you would use with the lights alone.
A 100ah battery could last as long as a week with your setup so running the engine when stationary may not even be required. Ideally with the addition of a single solar panel your power needs would be met entirely without starting the car.
Cheers Craig.............

Yes, Anderson Plugs are definitely the best way to ensure reliable charging of the van battery.