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Amp On Signal Wire (turns on amplifier)
Well I'd imagine with your OEM set-up this would turn your OEM amp within a short time after your Head Unit powers on (to prevent a pop). However using a car pc I'd expect you wont need this, or instead will need to connect it to your ACC/Ignition Line (Preferably with a delay circuit attached schematics can be found in the Hardware Development forum I believe)
In your OEM set-up this would control the deployment of your Antenna depending on if your radio is on or off. Unless you plan to hook up a radio to your Car PC this is largely unneeded. If you do you'd need to do this you would most likely have to put a switch on the ACC/Ignition line or use something like a phidget interface controller to control it through you pc.
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Battery (this ensures you keep your presets when your car is turned off)
As far as I know you'd connect this to your PSU instead of your Head Unit.
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Illumination Constant (wont dim when lights are on, most cases you would use this)
Illumination Switch (will dim your radio when your lights are on)
This i would imagine is largely useless unless, obviously if you wanted to make your screen dim at night (ergo when the lights are on) Not entirely sure how you'd go about this though
Connect it up to your Power Supply, this is what tells it to turn on/off depending on the status of you key.
Sorry if I missed the point of your question, I should have been in bed 2 hours ago >.>