My 1954 switches turn on by turning the key counter-clockwise; my 1955+ switches that are for non-foot-start vehicles turn on by turning the key clockwise. Maybe the direction of rotation is part of the problem?
In any case, a bench test of the switch (as suggested above) is the best diagnostic.
Do you know the year and application of your switch (car/truck)? There is usually no problem using a 12v switch in a 6v application (unless it is a 12v switch with a built-in ballast resister being uses in a 6v system - not your situation).
Tim