A humbucker has 2 wires coming from it. It will have one that is insulated and the other is a braided wire that is wrapped around the other insulated wire. Sometimes cheap pickups will just have 2 insulated wires but it sounds like you have the kind with the braided ground wire.
The insulated one goes to the tip of the input jack. The other one goes to the ring of the jack. The ring of the jack should also connect to the bridge, supposing it is metal.
If you can't figure it out or my assumption about the pickup is wrong then you must post pictures of the pickup and wiring it has.
I should very much like to build a mandolin as well. A diddley would be acceptable. I'd love to hear some more details about your build!
