Gas gauge and temp gauge stopped working at the same time

Loss of backlighting is a separate problem. maybe inst' panels chassis ground is both problems. The small screws that attach circuit board to housing are part of the chassis ground path. So depending on your circuit boards design,,, poor connection at one screw could inop limiter and a lamp. Boards with plug in limiter typically have a screw right there at it.
We've seen examples where the limiter stuck closed and a small copper trace on the circuit board served as a fusible link, burned open before killing the gauges. Where the limiter is mounted inside a 3 post fuel gauge,, there's a tiny piece of wire in there that will do the same.
Let us know what you find. Good luck