Dash/Instrument Illumination: Step by Step Search

It could very well be a break/ crack in the board. But you can fix that, easily. That is, if you can solder. As I said for this type work, and really, ANY automotive soldering, you should not only have "the usual" --a good iron or gun, and "radio" type solder, but you should have some liquid made for electrical soldering flux. THE PASTE you buy at plumbing and other places is ACID, do not use it. And you may not need it.

You can scrape places clean say, every couple inches and move your ohmeter along the trace to find a break. Then just solder a wire jumper across the break, or across the whole trace.

I agree with cudamark---bench test it. Get your wiring diagram and identify and mark the switched key power going to the board, and make a note paper of the connector pins. You can jumper power to such as the turn or high beam indicators, the gauges, use resistors as senders to check the gauges, everything.