.... The other two gears are found a cable slack and cable taut. [emphasis added]
A quibble. While I agree that the three speed positions are very forgiving, the term cable taut might cause problems. The cable pulls on a sliding clutch that turns with the sprocket and rides on a plain (not ball) bearing . It's designed to operate only at the load generated by the clutch return spring. Low gear is properly located with the clutch pulled all the way to the right (out) but the cable shouldn't actually be any tighter than that. If the cable is pulled to where it's under tension, that increases the load on the clutch bearing causing excess drag and wear.
So the correct 1st gear position is better described as just short of all the way to the right and not quite taut.