Your photos do not show a pressure tank located on the outlet side of the pump. Without a pressure tank, there is no provision to absorb some of the higher flow rate the pump is capable of supplying, vs the lesser flow rate exiting out through a single garden hose.
A pressure tank also provides storage of pressure whenever the pressure switch has shut off the pump while the outlet faucet is closed. Currently, stopping flow through the hose, will cause pressure to rapidly rise to the pressure switch cut-out pressure (50 psi), resulting in the pump shutting down, but without any provision for pressure storage, pressure will immediately drop to 0 psi and the pump will become re-activated. This rapid OFF/ON cycling will be continually repeated until flow is again restored through the hose, or the electrical power to the pump is shut off manually.
The packaging specifies the pump is capable of 630 gallons per hour, which is equal to 10.5 gallons per minute. That 10.5 GPM is based on 0 vertical rise of either the suction line before the pump, or to the outlet line exiting from the pump. Since there appears to be a substantial (? Feet) elevation rise between the water source and the pump inlet, the pump will then be actually capable of less than 10.5 GPM.
With no pressure tank, to prevent cycling, the water consumed will always need to equal or exceed the flow rate the pump is actually capable of supplying. I anticipate if a 2nd garden hose spigot is added to the left of the Tee, feeding two hoses at the same time, will likely match or even exceed the pump's flow rate capacity.
Adding a pressure tank, will reduce the cycling frequency whenever the flow rate is less than is being supplied by the pump. A larger pressure tank will result in less cycling compared to a smaller PT.
A pressure tank of any size however, will also allow the system to operate automatically, simply by opening or closing the spigot, without any need for disconnecting power whenever no water is needed.
