I had a similar experience with a replacement Sureflow pump. The original pump (about 12 years old) had an adjustment screw that allowed you to set the pressure at which the pump would turn off when no water was flowing, which was useful. However, the replacement pump had two adjusting screws. The second was, as I understood it, to set a bypass pressure, so if the desired pressure set by the first adjustment screw was reached when water was flowing, it would relieve some of the pressure by allowing some of the pumped water back into the inlet chamber, hence preventing the pump from cycling when in use.
The instructions warned that if the setting of the bypass was incorrect then the pump could run continuously without any water actually being pumped to the faucet.
However, I could not get the settings correct. The pump would sometimes not work
until it was given a knock, and other times would keep running with no water flowing – as you’ve reported.
My pump is very difficult to access, so after many frustrating attempts at setting it up I eventually cut my losses and fitted a whale pump, which has worked perfectly since.