Ok, now we're getting somewhere. We might be able to eliminate both tone pots and the capacitor and the solder/wire connections to the fore-mentioned, why?, because we know the bridge pickup has the same problem and that little sweetie does not run through the tone pots if it's wired traditionally. :) We can elimanate it is the pickups, because it is highly unlikely all three Apaches have the same fault.
We are now narrowed down to the switch, volume pot, jack, and their connections too. Since we know it does it on all 3 pickups we can also eliminate the pickup's ground wires going to the back of the volume pot.
Again this leaves us with the switch, volume pot, jack, and their connections. Now I don't think it's the switch itself, because all 3 pickups do this so the odds of the switch having a weak connection in all 3 (or 5) positions is highly unlikely, and the pickup's hot wire connections to the switch are probably good because the odds of all three hot wires to the switch being weak are highly unlikely.
Here are the connections that need to be checked &/or re-soldered - 1. The hot wire from the switch to the volume pot's outer lug. 2. The hot wire that connects both master hot tabs on the switch itself. 3. The ground wire from the volume pot to the jack. 4. The hot wire from the volume pot's center lug to the jack. 5. The volume pot itself. 6. The jack itself.
I strongly feel it will be solved in one of those 6 steps. Wiring straight to the Jack is a good start, and if you have an extra volume pot, there's no need to install it but wire it straight from the pickup to the pot and then to the jack.
I'm betting strongly this is a faulty volume pot or the jack, the jacks used if it was MIM are junk. If you get a soldering tool, make it a small 25w and use the chisel or flat-head screwdriver tip, liquid flux is your best friend to help the solder flow. You can clean it all up when you're done with q-tips and isopropyl alcohol 90%, and she'll look all pretty when your done.
Using an ohm meter, the Apache's neck should read about 4.5 to 5.0 at the output jack with the tone and volume controls set to max. Good luck. :)
WR