Wild guess:
It's a reliced pickup with brass plates under it that are connected to ground. AFAIK the plates do almost nothing besides grounding the pole pieces, if they indeed even do that. Grounding the pole pieces makes it so if you accidentally touch them while playing, they won't make noise.
So check if everything is grounded correctly. Use a multimeter in continuity mode. Black probe inside the jack, red probe to pots, screws, bridge, strings, string tree, tuners, ashtrays, pole pieces, etc. Everyhting should beep. If it doesn't, it's not grounded. Ungrounded parts make noise when touched.
I imagine the cavity and pickguard aren't shielded. If they aren't, you will hear noise when you don't touch the strings/bridge/jack/pots, and the noise will go away when you touch any grounded part (the opposite of what I described above).
If you hear a constant hum regardless of what you do, 9 times out of 10 the ground wire has slipped out from under the bridge.
The above should cover most noise occurrences. Hope it helps.