Non-A/C? I'd try cleaning the switch first, should be able to bench test and make sure it's not something else like the resistor.
Make sure the switch bezel has a good ground. I know on a 65-66 with a 3 speed fan that the bezel mount to the dash is ground to complete the circuit. If the paint is real thick on the dash or screws not tight, this can cause issues with the fan.