Jazz Bass Noise

[SuperSeagull]

My Fender Flea has developed some noise - more of a hum than a buzz. It is present as soon as the bass is plugged in and only goes away when either or both of the pickups are turned fully up. I'm used to having some buzz with single coils which goes away when the pickups are balanced volume wise - this is different. It doesn't change when I touch a string or other metal part. I have checked the continuity on the grounds of each pot and to the bridge. I've tried different leads, different amps, cleaned the pots and had a good nose around in the control cavity for anything obviously awry. I'm at a bit of a loss now.