Hi Bob,
This can happen when the gasket between the pump and the pressurized line is not fully sealed. that gasket/valve can slowly leak water back into the pump and then the pressurized side loses pressure. At some point, the pump starts up again. How old is that pump? You might just need a "Valves Kit", to replace the valve. There is also a Diaphragm Kit if it's more serious. It has to leak past the value first, and then back through the diaphragm. So if it's old enough you may need to replace both.
This can happen when the gasket between the pump and the pressurized line is not fully sealed. that gasket/valve can slowly leak water back into the pump and then the pressurized side loses pressure. At some point, the pump starts up again. How old is that pump? You might just need a "Valves Kit", to replace the valve. There is also a Diaphragm Kit if it's more serious. It has to leak past the value first, and then back through the diaphragm. So if it's old enough you may need to replace both.