Completely stumped

[phill 92]

Whilst working on my car I've noticed my fuel pump tripping on despite having no ignition, its been doing this for a while now and my battery eventually ran flat. I took the battery out and put it on charge and returned to working on my car. Then it tripped again?! the noise is like a solenoid activating. I can't figure out how this is activating with no power? is it time to replace the pump? I'm pretty sure its the fuel pump located just behind the drivers side headlight?

Any help would be appreciated again! I honestly have no idea what is going on!