I tow a Ford Explorer and I usually start the engine and shift gears when ever I stop for fuel or stop for lunch and then do so again when I stop for the night. Ford does not say I have to do this, I like to charge the battery and to circulate the transmission.
Twice in my travels when I have been driving for two or three days and not running the engine I had a dead battery when I got to my destination. It caused much aggravation to get the toad jumped off and everything reset on the computers.
So for me, starting the engine is peace of mind and I've never had a problem when I've done so. I have a 120 gal fuel tank and I usually fill up when I get below a half tank. I also need to get up and walk around by then.