A water pump that cycles on and off rapidly is typically caused by a failed accumulator tank, small leaks in the system, or a faulty pressure switch. Check the accumulator tank first, then inspect for leaks throughout your RV's plumbing system.
Everything you need to know about RV plumbing systems from fresh water supply to waste management.
Shurflo 4008 pressure switches fail from frequent cycling. Replace the microswitch for under $20 from Amazon. An accumulator tank reduces cycling and extends pump life.
Yes, using a 3/8" braided supply line on your pump discharge will reduce flow rate compared to 1/2" PEX, but it can work effectively for vibration dampening if sized appropriately for your specific application.