How do I drive 60 back-to-back LEDs (Christmas Lights)?
What you are searching is a H bridge driver.



It's typically used in motor control application.

Here is perhaps something that can get you started with some good example There.

It is meant to drive motor, but will work the same with your LED. CW direction would be one LED type and CCW would be the other LED lighting up.

You also need to limit the current. Check whether those LED integrate the resistor (which is often the case in those led string). Otherwise you will also need current regulation.