All KF overdrive solenoids are fused at 20 amps, not 30 as was (and often is) stated. Check the diagram shown below which is right out of the KF shop manual. A 30 amp fuse is longer than a 20 and likely would not fit the holder on the relay. The overdrive relay has four terminals, the solenoid has 2.
Here's how I would explain the electrical workings;
There are two circuits: The control circuit and the controlled circuit. The controlled circuit (the one that provides 6v to the solenoid) is from the hot wire terminal on the starter solenoid which is connected directly to the battery, then through the fuse (1 BAT.), to the normally open contacts on the relay. The other side of the normally open contacts on the relay (4 SOL.) goes to the solenoid (4) on the overdrive unit itself on the back the transmission. All the wires used on the controlled circuit must be 12 gauge - that is very important.
The control circuit (the one that controls if the solenoid gets energized) is from the hot terminal on the coil (-), so it only works when the switch is on, over to one side of the coil on the relay (2IGN). The other side of the coil on the relay (3TH) goes to the normally closed contacts on the kickdown switch (A), then to the normally open contacts on the rail switch (the O.D. Lock-out Switch) which close when the cable is pushed in, then to the terminal on the governor switch which is normally open. The other side of the governor switch goes to ground. This circuit is wired with 16 gauge wire.
When the car reaches approximately 30 mph, the governor switch closes, which provides a ground for the relay coil circuit, hence energizing the relay causing the relay contacts to close (they appear to be closed in the diagram but they are normally open which means they close when coil is energized). This puts 6 volts on the solenoid which then pushes the pawl into the control plate in the OD unit. Let your foot off the gas and the pawl slips in and the car operates in overdrive.
There is a third circuit which is used for kickdown. There is a wire which goes from the distributor side of the coil(+) to the normally open contacts on the kickdown switch (B) which then goes to a set of normally open contacts inside the solenoid (6). When the solenoid is energized, those contacts (6) close. When you press the accelerator all the way down, it closes the contacts on the kickdown switch (B) which provides a path from the coil (+) to ground causing the engine to misfire. The torque reversal allows the pawl to retract and the car is no longer in overdrive. This circuit too uses 16 gauge wire.
Here's a diagram of the circuit