It sounds like your "switched power" leads from the Aiwa are connected to your car's lighting circuit, not what you want. They should be connected to any circuit which energizes when you turn your ignition key to the 1st position, ("accessories on"). There should be such a wire that went to the old radio and is flopping around somewhere nearby.

The "illumination leads" go to a lighting circuit - maybe you got that confused with the "switched power"?

Get a cheap 12V test probe from Radio Shack or an autoparts store and use it to find the right wires from your car. Take a bit of care with this, as getting it wrong can blow fuses or possibly fry your new radio. Make sure the ground wire goes to metal, not to some wire coming out of a harness. Live circuits can act like grounds but will cause problems if used as such.

Another option is to get a harness adapter from Crutchfield. With the purchase you also get all the free tech advice you need to hook it up right.
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'84 '285' rice-eater with lotsa hp & performance goodies