I often travel solo during the race season and I use truck stops,rest areas and Walmart to get some sleep and then move on. If dear wife is my passenger we stay in campgrounds and relax.
I keep my water tank full. How much gas it would save if empty? can barely be measured. I kept track of each tank of fuel for the last 35K miles. Towing the Jeep, 18 foot trailer, empty tanks, full tanks, my 30 ft Cambria averaged 8.5 MPG. Towing my Jeep to Las Vegas,250 miles vs not towing my Jeep and the mileage was the same. Seriously doubt that an empty tank of water would save much, hitting passing gear a few times would eat up what you saved.
I fill 'er up and go, when it needs more I stop and fill "er up again. If my intention was to pinch pennies I would have never bought a motorhome.
The first time i sanitized my tanks also happened to be the time i had an allergic reaction to bug bites that I put "deet" on after I scratched open the skin. Thinking I should shower ,the bleach in the water was enough to swell my arms up like Hulk Hogans.
a 2 hour ride home to urgent care was the most painful time.
Why I am telling you this, I don't know.