Use a diode coming out of the car wiring so it does not feed back into the unintended light bulb. Then you can join them together at the common bulb that will do the blinker and Brake lamp. The problem you will run into thought is the brake light will override the blinker causing it not to blink on the trailer when the brakes are applied.
Edit: You could run the power to the lights through a relay and when the blinker power is applied it would cause the relay to energize disconnecting the bright causing it to blink even with the brakes applied. You would need 1 more diode and a jumper to make it work.
Edit2: The above edit idea is giving me troubles, need to work on it more.
Edit3: There is a kit that they sell for $25 that lets you put them together into the same wire. This would be much easier then running a bunch of relays. I could not get it to work properly on homemade wiring with less then adding 4 relays and 6 diodes.
http://www.etrailer.com/Tow-Bars/Tow-Ready/118158.html