I wouldn't worry about. Have run pumps dry on multiple units, my father did it for over a week on his fifth wheel. Have only ever replaced one water pump and that was back in the 70s on my father's old Franklin TC.
Odds are if it is cycling with air purged and no leaks, it may have gotten a piece of trash in the check valve or it is sticking from the heat build up.
Following the parts diagram, you can easily take the pump mechanism apart to check the valve.
In regard to carrying a spare, I wouldn't as space and weight is too much of a premium. Not sure about yours, but if my pump did go out, it would just be an inconvenience since I can still get water from the drain valve at the back of my camper even with it on the truck. So it wouldn't ruin the camping trip until I made it to a camping store. Couple of wire nuts, two hose clamps, and two mounting screws so can change it on the road with "ease". (well as easy as I could at home).