How to Fix Pickup Crosstalk

So I recently got a new instrument, it's got 2 humbuckers, 2 volume controls and a 3 way pickup selector, but I've noticed that when I flick the switch to the neck position, and roll the neck volume all the way down, I can faintly hear the bridge pickup, and vice versa in the other position. This is especially prevalent when I'm playing with gain. With some googling I think I found that this might be called crosstalk, so I'm wondering now how to fix it. If anyone has any advice I'd greatly appreciate it, thanks!

 

In this case I bought it used but almost new so I'm not able to return it. I think this is probably an issue from the factory because it's difficult to notice.

I worked it out mainly after playing with some gain on. So I rolled the neck pickup all the way off, had the bridge pickup on, and flipped through the switch. Bridge solo and both pickups on produced the sound of the bridge pickup as expected, when I flipped to the neck position I was still getting signal through my amp, just with less gain, I double checked this by tapping the pickups with a screwdriver as well. The opposite was also true with the other pickup.