Begin by immediately shutting off the pump and closing all water valves leading into it. Check the screws around the pump head and tighten them if necessary. It's possible that the switch diaphragm at the front of the head has been punctured by debris coming through the water inlet valve. Verify this by unbolting the switch diaphragm housing from the pump. The gears of the drive assembly should be visible in the water pump with the housing removed. If there is water or condensation on the gears, then the switch diaphragm has been punctured. It's a thin plastic plate within the unbolted housing. This should be replaced, and the drive assembly will have to be serviced by professionals to remove the danger of long-term water damage.
Pump runs but causes no water flow
First check the bleed valves connected to the RV's water tank, hot water heater, and faucets. Engage them all to make sure that there's no air in the lines, preventing the pump from moving water. Likewise, make sure that the water tank has water in it. Turn off the water inlet valve connected to the pump and unscrew the disc-shaped in-line strainer that it connects to. Open the strainer and clean it of all debris that may be impeding water flow. Reassemble the strainer, connect it to the pump, turn on the water inlet valve, and start the pump again. If no water flows, then there's either a loose connection in the water feed lines which are preventing the pump from moving water, or the pump's housing is cracked and not able to create a vacuum.
Pump continuously cycles
The pump is cycling because it thinks it's not generating sufficient water flow. If the water shut-off valve has been closed, open it. If there is a water filter or purifier connected to the pump's input line, it will slow the intake of water, causing this problem. Water filters should be connected to the output port of the pump, not the input port. Finally, check the pressure switch. It should be engaging when the water pump has done its job, preventing it from cycling. Since there's no obstruction preventing sufficient water flow, the pressure switch's activation threshold is set too high and should be adjusted.