I had a similar problem on a boat years ago. What I put it down as was. The taco W lead as you say, sometimes T, is taken off one of the usually three coils within the alternators AC windings. When you start, the battery will be slightly low, the small wire going to the alternator will tell the voltage regulator to produce current so the inner coils work hard producing a strong AC pulse. As the battery comes up to full voltage, the alternator decreases output, and the AC pulse from the main wiring drops to almost zero, thus giving a week signal to the taco and false readings. This might not sound very scientific, but it seems what happened to my boat. My answer, I bought one of those cheapo Chinese tacos off ebay and epoxy glued a small magnet to the front crank for the sensor. It worked well for years and was still on when I sold the boat. I suppose to test this theory, the next time the taco gives false readings, try switching the lights on full to make the alternator work harder.