A dry or dirty cable could be the cause of a wild needle, especially at low speeds.
To remove the cable, unscrew the cap at the back of the instrument panel and pull the square-tip cable out of the cable housing.
Wipe the cable clean and apply a cable lubricant (1965 shop manual specifies B5A-19581-A and cautions against over lubricating) and reinsert it into the sleeve. Be sure the square end of the cable is fully seated in the driven gear at the transmission---you may have to rotate the cabel back and forth a couple of time---and reattach the cap at the back of the instrument panel.
For more information, see the discussion on this topic on the Vintage Mustang Forum.
submitted by a65ragtop