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Re: relay - yeah, well aware of the issues with the switch, both draining the battery and starting with them both connected. I've got a sweet system set up to protect against this though which I'll post about later. It's only a temporary measure used while trying to diagnose an issue with either our VSR or leisure battery without access to a multimeter (turns out it's almost certainly the latter) where the charging setup was causing the starter battery to boil.
I now have a multimeter, which is fun and am pretty certain the battery is at fault. With the manual switching set up and nothing else wired in it's never getting above 5v charge and is slowly discharging overnight despite being disconnected. We considered taking it to an autoelectric place and seeing if they could blast it with a grunty charger but some digging in the previous owners receipts it looks like it was already a reconditioned unit and most likely at the end of it's life. Thankfully we've been tipped off about 25% off a new deep cycle unit on boxing day so we're hanging out to replace it with that.
Well aware of the drain for the cooler, it has a male cig lighter socket for the power so I'll just wire input in with a switch to turn it on/off from the front of the van. We're not really going to use it too much and will be selling the van in ~6 weeks anyway, just trying to get stuff fixed up in a cheap+safe manner so we don't lose too much on it (already spent a bunch on panel/rust work, new tyres, new radiator etc.).
Edit: what @Emyr said.
You really should put in a split charging relay but you already know this I guess. A good one will prioritise charging the starter battery first before the leisure battery, but the alternator should charge both batteries and run the fridge simultaneously so I’m not sure your proposed additional 12v socket will bring much benefit unless the engine is running and the leisure battery isn’t being charged. The danger of a simple switch is that if you leave the circuit closed and try to start the van, you’ll be pulling power from the leisure battery as well. Leisure batteries are constructed of different electrochemical materials and designed for long, slow drain, starter batteries are the opposite, and they can’t be interchanged. So you would damage the leisure battery irreparably the first time you do this.
That aside, a 12v socket powering the fridge from the leisure battery will work best. Fridges are notoriously inefficient however so expect about 24-48h before you flatten the battery. (This would be preferable to draining the starter battery though). You can obviously improve efficiency by using freezer packs in the fridge and not opening it too frequently.