If this was me (and what I will do when I get a Ute setup ), for the pop top buy a 200ah lithium, 2000w inverter, so you can have luxury for remote or everyday touring, like an instant electric hws
Power: 1500W. This is a lightweight electric water heater with a perfect combination of inner quality and classical appearance, which applies for multiple demands of different families. 1 xInstant Electric Water Heater.
www.ebay.com.au
I wouldn't rush out to get one. I was looking into Electric instant hot water when we did our kitchen renovation the sales guy talked me out of it saying they chew power, he said they cost around $5 per day to run and most people switch them off. Not sure how true that is but he sure talked me out of it.
Yep they are instant hot water, but unlike the gas ones, they are NOT instant power use. They heat a small tank slowly the whole time, and then when you use it, it goes to full power.
For that model of HWS, physics shows it would take about 20 mins to heat its 7l of water from 15 to 55 degrees. BUT look at the specs. 1000/1500W. If it is like every other expensive, high-efficiency instant HWS, it will preheat the water at 1000W ( cycled) until you use it. But it is on ebay so that $80 chinese unapproved one may be better than the $500 approved, "efficient" models.
So those 200AH of batteries will last around 5 hours if you have hot water ready but don't use it, and about 2 hours if you wash the dishes twice.
Lithium batteries are being sold as the electronic wonder drug for 4wd power. It's great, but not really useful for anything that converts electricity to heat. That crap is only good if you camp at powered caravan sites.
For $80 try it at home. Get a free power pal to measure the power use. Oh don't touch the water when it is coming out of the tap. It may be "hot" in voltage as well as temperature.