LED strip - brake/turn same wire

You can also make your own with a time-out circuit in case you leave the signal on.
There are a few options on this page, including an integrator you can build. It requires a ground a wire.
s3.amazonaws.com/gpzweb/Lighting/GPZturnSigInteg.html

It would be easier to buy a second LED strip only for the running and brake light.

I yeild my time to the experts. 

For anyone in the future that wants to know how this turned out:
I ordered a Curt brand non-powered 3 wire to 2 wire converter. I connected the wires, gave it a test.... and it did not work. I should have read closer to the description that the converter I bought would not work for LED applications.
So then I went to the local automotive store and got this Reese converter:  Reese Towpower | 8507900 | Taillight Converter
That worked! 

So in case anyone runs into an aftermarket rear light situation where the signals and brake share wires, use a trailer converter!

Thanks, as always, for your help guys!

Glad it's working. Thanks for the update.  That will definitely help others, as more and more questions related to LEDs show up all the time. 

If you havent tried to install the trailer box yet, this is definitely a better choice.  shop.revivalcycles.com/led-dual-element-circuit I bought 4 of them for my bike lighting and they work great.