Okay, well this is how you want to do it if you are to run automatic lights in addition to the delayed-exit, and also be able turn the system on/off (diagram courtesy of an English gentleman by the name of Dereck who installed this in his Excusrion):
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Basically the switch in the left side is your on/off switch for the system, the autolamp sensor is the factory Ford control module, the stuff below the sensor is a DPDT relay (one control circuits triggers two independent power circuits at the same time), and on the right you have your factory headlights switch. What happens is that when the ignition is on and you on/off switch is also on the autolamp sensor will bypass the headlights switch and power up the lights independently of it, so if it's dark out there and you want your lights off while running the engine you have to use your on/off switch to shut the the autolamp sensor off, and if you want headlights during daytime (the autolamp sensor will not turn them on when there ambient lighting is good) you use your factory ignition switch. The autolamp sensor will obviously need to be installed in a location where it can "see" daylight good, the factory drills a hole in the dash pad and puts it under there so light can fall through that hole and onto the photocell.
As far as the relay goes you have two options:
a) if you want both your headlights and marker lights to be controlled by the autolamp sensor you either install a DPDT relay like in the diagram, or you just run two regular cheap SPST relays in parallel where you splice the sensor output wire (green in the diagram) into two separate wires so it triggers both relays at the same time;
b) if you only want the headlights to be controlled by the autolamp system just run a single SPST relay for the headlights circuit and don't worry about the blue and brown wires in the diagram that are used for the marker lights.
An important note on this: your gauge cluster illumination is tied into the marker lights circuit, so if you use the autolamp system to only power up the headlights your gauges will not light up unless you manually turn the marker lights on with the factory headlights switch.
Now onto the delay-exit lights - the factory uses a variable resistor to control the time the lights stay on after ignition is shut off, that variable resistor (along with the system on/off switch really) is integrated in the main headlights switch which looks like it could made to fit our trucks but may require some grinding on the plastic panel of the dash. If you would like adjustable time delay, but do not want to mess with retrofitting headlight switches, you can run an external variable pod like you can buy in RadioShack. For sake of simplicity both Dereck and I have chosen to run a fixed time delay, he opted for the 54k-ohm resistor that you see in the diagram and that gives him about 30 seconds of delay, while I installed a 100k-ohms resistor in my truck and my lights stay on for about a minute. As you probably figured it by now, there is a small capacitor inside the autolamp sensor, and its discharge rate depends in that external resistance - the larger the resistance the slower the discharge and so the longer the time delay, and this will take some experimentation on your part to find the exact resistance that makes your lights stay on for the amount of time you want them on.
The way all this is installed in my truck - I have converted my low beams to DRL mode (they are on all the time the truck is running), so I did not really need the autolamp feature of the control module, which allowed me to lose the on/off switch and also to install the control module inside the engine bay where it "sees" dark all the time - basically the system is always active when the ignition is on, and it also keeps the DRLs lit regardless of ambient lighting conditions. This greatly simplifies the install - the white wire that in the diagram goes to the on/off switch now gets grounded instead, and the sensor itself get spliced in my key-on trigger for the SPST relay I already installed for the DRLs so that the key-on 12V go into the sensor through its yellow wire, and then out the sensor and to the DRL relay through the green wire. Piece of cake really, and works awesome!
In case you're wondering where I'm getting my key-on voltages for all the stuff - since I converted to hydroboost I no longer have a need for a low vacuum switch, the harness for that switch has two 12V wires and a ground wire one of these wires (red in color) provides reference signal or something to the vacuum switch and I used it to power up my solenoid for controlling the recirculating door in the HVAC system, the green 12V wire in that same harness is what I used to trigger initially the DRL relay and now it triggers the autolamp sensor/control module. Why not the other way around? Cause when you ground the green wire you trigger the red "Brake" light on the dash, so in order not to see said light on all the time I could only use the circuit for something that draws so much power that the current flow is not enough to illuminate the light - the DRL relay actually pulled just enough current that the light would glow very dim (could only be seen at night with gauge cluster lights off), but the autolamp sensor draws next to nothing and lights stays off for good. There is an extra benefit to that too - when I'm idling for prolonged times in a parking lot or at home, I can simply put the parking brake on and the DRLs sut off - electricity always follows the path of least resistance, and apparently the brake light and the grounded e-brake pedal switch make for less resistance than my autolamp sensor or the DRL relay - current switches paths, illuminates the light on the dash like it should for the parking brake, and then goes straight to ground through the e-brake pedal switch, and the autolamp sensor loses its key-on power and a minute later my DRLs promptly shut off
Pics of the installed autolamp sensor to follow soon, apparently my camera batteries need recharging