Plenty of posts on how to clean the sending unit...driver, start your search engine!

My 300D had the identical problem, all due to a dirty sending unit. Sediment builds up at the bottom of the sending unit and insulates the contact points. If you clean out the unit pay special attention (and care) to the very thin nichrome wires and if you disassemble the float system to clean it, be certain the tiny wipers that run along those wires are correctly situated. Wanna ask me how I know??

Good luck, the force of the forum is behind you!