Here's a simplified wiring diagram of the 4-inch coil. The five cable wires are numbered to correspond with those on the plug, as seen in the second pic.
The inner coil is colored green. It connects to Pin 1 (red cable wire) and Pin 2 (black cable wire).
The outer and middle coils are colored red. They are wound from a single length of wire, but wound in two sections. It thus consists of two windings with a space between them of about a half-inch. Electrically, they would be considered as two series-wound loops with an air gap. The smaller half is wound tightly against the green coil. The large half of the red loop begins at Pin 4 (white cable wire). At its end, it wraps around itself, then heads to the center of the coil. There, a small hank of wire is in a loose oval shape and seems almost randomly wrapped about the center of the oval. From here, the red coil continues with the smaller half of its winding. The smaller loop ends at Pin 3 (gray cable wire). Additionally, the red coils are paralleled by two capacitors. a .22 uf and a "223" (.022 uf). At the point where the wires exit the outer jacket of the cable, the gray wire is stripped of insulation so it contacts the cable's shield.
Finally, a short length of red-colored wire (drawn in yellow for clarity) is connected to Pin 5 (green cable wire) and randomly wraps loosely around the inner green and middle red coils. After a few turns, the wire dead-ends without a connection to its far end. I did not see the green cable wire connected inside the detector either, so I don't know the purpose of this wire that is apparently not actually connected into the circuit. I may have to open up the Time Ranger again and see if I missed something.
-Ed