That is a very different application and not one that needs a dual-polarity power supply to work?
According to the description, the arrow LEDs work on either polarity.
If I understand what you are saying, you want to use two wires and have one arrow working on one polarity and the other with the opposite polarity.
I think that should be possible just by adding two rectifier diodes from the two inputs to common, both the same way around (eg. both cathodes to common or both anodes to common).
You should then just be able to use the other two terminals and the lights should be controlled by the power polarity.
For info, that same board here, about a third of the way down the page:
**broken link removed**
Translation of the description: