Steve is probably right, this is the most common cause of the pump cycling. If you have a way to shut off the water behind the pump to eliminate any leaks upstream you can try that first. If it turns out to be the pump, try to get the make and model number, most RV dealers stock repair kits. The swap is easy and takes no more than 10 minutes once you have the pump out.
2013 RAM 3500 Longhorn Dually, Andersen Ultimate 5th Wheel Hitch,2014 Trilogy 3650 RL, 8000# axles, disk brakes, I.S., 960 Watt Solar