Is the hum affected by you touching metal/strings/bridge? If the hum goes away when touching metal you have a shielding issue, if it gets louder you have a ground issue. If the noise remains unaffected it is probably just due to the single coils picking up electrical noise and nothing you can do, but I would double check the wiring anyways, specifically the ground wire under the bridge. The pickups become humbuckers when both turned on full.
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