The tacho internally is not gear driven but driven by a spinning magnet so running it in reverse shouldn’t do any harm. Try running it both directions with your drill, I’ve just fixed my sons CB 550 tacho and it was the rivets holding the magnet assembly that were slightly loose. If I put pressure to one side of the cable where it connects to the unit while the engine was running the tacho would function but as soon as I released it the tacho would stop.
If you do strip it down don’t go mad lubricating it, just a few tiny spots on the bearing surfaces.