Hi there,
The reason you cannot find the wires at the back of the unit (OEM radio harness) is because the factory system uses an amplifier (located to the left of the glovebox behind the dash panel).
You have a few options here.
1. Use the low level (pre-outs) of the aftermarket radio to send signal to the 6ch factory amp.
2. Leave the existing wires that the previous owner ran to the back speakers* and run new wires to the harness running into each front door (behind kick panels, this is where you will find the wire colours you mentioned) *Please note that the factory rear speakers are separate components (tweeter & mid/woofer) and the mid/woofers are 2Ω. Meaning (a) that you cannot just run a full range signal to both (you'll blow the tweeters) and (B) an aftermarket radio should not have 2Ω speakers ran off it.
3. As above but run new wires to the harness that plugs into the factory amp. (this is not the easiest option as it is very tight and not much room for making the required connections. But again you have the issue of the factory rear speakers.
To do it properly you really have two options:
1. Use the low level (pre-outs) of the aftermarket radio to send signal to the 6ch factory amp. I have the pin-outs you will need. Let me know if you want to take this route via PM and I'll email them to you.
2. Replace the factory rear speakers with aftermarket 6x9's, connect these to the previous owners wires. Run new wires to the kick panels for your fronts. *You should also make sure you have the polarity correct (+/-) on each speaker other wise it will sound very average.
Let me know if you need any more help.
(Also note that the IS300 is different, only 2ch low-level from the unit and volume and fade controlled by OEM radio)
Van-daviz