Hello Adam,
If the pump continually runs for a moment every 6 seconds or so and will only stop when you turn the power off, then I suspect it is neither of the issues my illustrious co contributors have mentioned.
What is happening is the pump is able to get the water pressure high enough to turn off, The combination of the plastic pipe work and designed air caps in some appliances gives the water system some elasticity, but there is a leak of some sort which is allowing the pipework to lose pressure which is triggers the pump again.
Now you have said you cant find a leak anywhere, This can be the the apparent case so I suggest you look again carefully. But also the problem can be the non return valve in the pressure switch. If this is not closing completely then when the pump turns off, it may allow some water back through to drain back to the tank - hence you don't see it.
In many cases with careful disassembly of the pressure switch you can clean it and recover the situation, but if that doesn't work you could insert a new non return valve in the pipe work between the pump and the switch, or of course replace the whole pressure switch.