A fridge switch or some device to shut off 12v supply from tug to fridge when engine is stopped is a must, otherwise the fridge will suck the battery dry in a hour or so, enough so you won't start the engine ........
Ideally a dedicated cable 8 B&S at least from tug battery to van fridge with anderson plugs on draw bar and anderson plugs at rear of fridge to allow a cable size step down to fridge connector where you fit a Fridge Switch is the best way to do it, a good supply of power is assured and does allow any vehicle to tow..
The fridge switch is easy to set up, basically plug and play but some prefer a relay that cuts off at a certain voltage but when the battery is also a cranker I prefer ASAP before the battery drops................. I have used a relay so with parking lights on the fridge was on, turn off lights fridge was off, never forgot as car beeped like crazy when shut down with lights on but that van had a lights wiring loom behind fridge and I had a relay doing nothing......
Other wise when you stop and do your walk around, you pull the plug each time and if you walk around before you leave then you plug it back in, a walk around each time is a good idea especially if you leave the vehicle, some people think its funny to play with your hitch so it pays to check ....
Never drive with the gas turned on, ever....
Quite a few threads on the subject on here......... if you can find them.