Where would one get such a device/connection for under $10?
Google your car manufacturer (also try the vehicle model) and the keywords "aux input" or "auxiliary input". Most manufacturers have standard connectors on the back of their head units that don't change from year to year. Mazda, for instance, used the same connector (CN702) on all their head units from 1994 to 2001. (After 2001 they started using a different connector that's not as simple to use.)
Once you know the connector pinout, buy a stereo mini jack from Radio Shack, connect the left channel of the jack to the left pin of the connector, the right channel to the right, and the ground to ground. You're almost done. There are usually two pins of the connector that you need to connect together to let the head unit know the "CD changer" has been connected up. If the head unit has a CD changer button, you usually just connect the two pins together. If there is no button, buy a switch from Radio Shack and use it to connect/disconnect the two pins. BTW, to avoid having to solder to your head unit, you can buy empty connectors at Radio Shack or an electronics supply place. They're either DIN (round) or Molex (rectangular) type.
Here's a web page going into more detail about how to do this:
http://carstereoipod.blogspot.com/