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|I agree with Answerman that it is not likely to be the tach. It is most likely something in the engine compartment. I would check all the electrical connections to see if something is loose or corroded. A bad coil or resistor is also not likely, though possible. Sounds like the alternator may not be charging the battery, which would cause the battery to loose charge faster when driving than when sitting idle. Another possibility is the electrical switch on the steering column. I have had these go bad on me. This can be more of a problem when driving than when idling because there is more bouncing around which can cause the connection to go bad. Hot wiring directly from the battery to the + side of the coil will bypass everything, which will at least show you the general area of the problem.
I also had a problem like this when I first started my car after several years sitting. In my case it finally turned out that the engine was running way too rich at speed so the plugs were getting fouled causing misfires. adjusting the carbs fixed it.