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Yes. To test phase, you need to see whether a coil has a positive or negative charge induced as metal moves toward it, or away from it. You can use the DC voltage setting on the meter (usually the lowest setting, typically 200mv), or by the watching the change in the resistance reading. You're not really changing the resistance to the degree that the meter tells you as you move the field, but the voltage generated will change the reading none the less, and typically show a more substantial change than the voltage reading.
So set your meter on the appropriate resistance (i.e., 20kΩ), hook the red lead from the meter to the red wire of the Duncan pickup, and the black (ground) lead to the green wire. You should get 4-8kΩ reading on the meter. Slowly move a screwdriver, scale, any iron tool down toward the adjustable screw bobbin (analog meters you can move quickly here, digital meters you'll have to move slower with slower sampling rates). If the Duncan pickup is made as normal, you should see the resistance reading rise when you move toward it, then fall as you move away. This is normal, standard phase, though there are certainly some makers that set theirs up in reverse. If you get the reading I mentioned, you have just confirmed that the green is the ground lead of that coil, and the red is hot.
Move to the black and white wires. Just for sake of learning and demonstration, hook the red lead of the meter to white, and the black lead to black. Now on a normal Duncan pickup, you would likely see the resistance reading fall as you move a tool toward the solid slug coil, and rise as you pull away. This would tell you that you have the coil hooked to the meter in reverse phase from the other one. So that means the black lead should be hot, and the white to ground. To confirm you can hook the white pickup lead to the black (ground) meter lead, and the black pickup lead to the red (hot) meter lead. Now you should see the resistance reading rise as you move toward the coil.
So jot these notes down as you test, and you have green ground and red hot for one coil, and white ground / black hot for the other. Hook a ground and a hot together (like white and red), then you are left with a series wired humbucker with green as final ground and black as hot.
So to check your Jackson pickup, it's reasonable to assume the bare is ground and white and red are opposite leads in a series wired pickup, though not guaranteed. One side of one coil could also be dedicated to the bare ground, the white or red be the end of the opposite coil, and the remaining wire a coil split, connected to the junction between the two. I'd guess that as unlikely, but you can check easily enough by testing the resistance between the three leads. For example, if the resistance were say, 10kΩ between the red and white, no conductivity between bare ground and either of the others, and direct conductivity between the ground wire and the base plate, then the ground is just a ground and not dedicated to either coil. This is probably the case, and to avoid typing another chapter I'll leave it there. If not, we can go through other options then.
Then hook the red wire to the red meter lead, and the white wire to the black lead. If the reading goes up when you move metal toward the pickup, then red should go to hot and white to ground to match the phase of the Duncan. If it goes down when you move toward, that's telling you you have it hooked to the meter in reverse, and red should ultimately be ground and white to hot.
It's really simple, and I don't even keep track of color codes anymore because it takes me less time to hook each pickup to the meter than it does to pull the presumptive charts off the shelf. It's a 15-30 second test for a pair of humbuckers, and if you plan to do work on electronics often is worth understanding.
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Eschew obfuscation, espouse elucidation.
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