If you have a meter or a continuity tester, you can suss out the connections.

I'm not familiar with the Ibanez wiring, but I suspect that you have tied the 'hot' lead of your Jackson pickup to something that should not be there.

Most 3-wire humbuckers have the 'hot' lead from one coil, the 'return' lead from the other coil, and a Ground lead that only connects to the frame of the pickup. The Ibanez may be a different beast altogether, possibly bringing the inter-coil connection out on one of the wires, and the switching circuit may need to be modified a bit to accommodate a standard 2-wire humbucker.

If you can get an Ohm-meter, it can really help you make sense of this. Without a schematic of the original circuit, you will have to carefully trace everything out for yourself. The one advantage to this is that you will gain a better understanding of the circuit.