Fuses are not intermittent. When they blow, they're done. They don't magically fix themselves. Also, there is no separate fuse for just the gas gauge. A blown fuse would affect many things on the dash.
With the consistent symptom you described, that is typically of a defective sending unit in the gas tank. Chrysler had a similar problem that took less than ten seconds to fix, ... Once the unit was out of the tank. I suspect yours can be fixed too but I never did one on a GM product. If it is riveted together you'll have to replace it.