Success! I poked around the net and found this page:
Car Audio Wire Diagram Codes Toyota - Factory Car Stereo Repair - Bose Stereo, Speaker / Amplifier Repair
The 10 pin and 6 pin turned out to be exactly the connectors I was looking for, I double checked them and they seemed to fit my internal car stereo perfectly. So I draw a chematic over how the cables should be joined together and went down to my garage to try this. And yes, it works! So now I can enjoy the Toyota's excelent RDS radio, as well as play MP3s from my JVC car stereo! Hurray!
Here are a simple description of the connectors behind my integrated Toyota stereo: (The view is when looking on the connectors on the device itself)
10 PIN connector:
[_4][_3]________[_2][_1]
[10][_9][_8][_7][_6][_5]
6 PIN connector:
[12]________[11]
[16][15][14][13]
There is a third connector as well, but it doesn't have anything to do with the third party car stereo we are inserting
What these numbers mean:
1: Front speaker right +
2: Front speaker left +
3: 12 V +
4: 12 V constant current (straight from the battery, aka backup/memory current)
5: Front speaker right -
6: Front speaker left -
7: Ground
8: Not used
9: Not used
10: ILL + (unknown purpose)
11: Rear speaker right +
12: Rear speaker left +
13: Rear speaker right -
14: Rear speaker left -
As it turned out, all my cables could easily be inserted directly into the Toyota connectors and taped together in pairs with their matching mate from the cars own wiring. Therefore I saved myself some cutting of wiring, buying of any converters and extra cables etc, and a whole lot of time!
Only problem was that the new car stereo was slightly to large, and thus the ash tray is now a couble of milimetres closer to the gear shifter :S
.. Oh and by the way, my car is an Toyota Yaris Verso 2001 Modell (European), but it seems the car stereo from toyota really hasnt changed since the first Yaris, and the Verso has the same one that the ordinary Yaris has.