So, 0.004"/0.006" is mighty tight. There is much happiness to be found at six&eight.
If the tach is down, look for other vacancies in the electrical stable: various lights, horn, instrument illumination, "warning" lights?
Even new batteries can cast aspersions on our existence . . .
With a digital voltmeter check 1)key off; 2) cranking; 3) idle; 4) some rpm, like 2500 or so.
(Oh, I can't recall how many times I've read, "Unplug the Power Commander and try again.")