I'm fairly certain there's no leak. I can't hear one and an inspection
at each of the junctions while the pump is on with the faucets all closed shows no moisture at any of them. I'm less certain about the tank side as, correct me if I'm wrong, there could still be a leak without the presence of dripping water. But that's something I'll have to wait to check after I run the tank dry again. I went back and tightened the clamps once more just to be sure, but the problem still exists.
Nigel's post was pretty illuminating. There's no expansion tank or non-return valve before my seaward
heater. Just to check I took the heater out of the loop altogether, but that actually made the problem worse, causing the pump to just run continuously rather than intermittently with the faucets closed. The only thing is, the way the material reads the expansion tank and valve are only there to prevent the expansion valve on the tank from weeping when the water is hot, which it isn't at the moment. So I'm not sure if that's a likely problem or not.
I've actually ordered an instant on heater which I was planning to replace the seaward
with. After my little test today it looks like that may be a problem as to some degree the seaward seems to be acting like an expansion tank itself. I'm not sure if Simon may actually be correct that I should put an accumulator in the mix, as outlined in the material above, to serve as an expansion tank.
I should also add that I'd disassembled this prior to posting
and there aren't any problems with the internal components.