If it were my sign, I would start by seeing if I could find the manufacturer, or who the manufacturer is -today- and getting in contact with them about the board. A nicely worded email might open up some information. I would also post all the information you could about the sign, including clear front and back pictures - to the Electro-Tech forums (http://www.electro-tech-online.com/datasheets-manuals-parts/);
you might find someone who was an old employee who built the sign, or maybe has some docs they could send to you. If neither of those options worked out, I would then take on the task of reverse-engineering the schematic from the PCB; likely it isn't too difficult - much of the schematic would be duplication (likely for a set of columns). I am willing to bet the device is serial-driven in some fashion - once you had the schematic laid out, it would likely be fairly easy to figure out how to interface with it.