Noisy P pup in 3-way switch help?

[hooky_lowdown]

 

I've recently got an 80s Aria Pro ii with PJ pickups, has a volume, tone and 3-way pickup toggle.

 

Bizarrely, when the 3-way toggle is in middle, and on the jazz pickup there's no noise. However, when I select the P pickup I get noise (60 cycle hum). I checked and it's definitely the P pickup making the noise, and the jazz soloed is pretty much noiseless. Goes beyond logic. Anyone know why I'm getting noise only from the P pickup?