Hi, We had a similar problem when we purchased our car. When we remove the steering wheel we found that the plastic on the horn contact pin assembly was cracked. If it's cracked Classic Industries sells the kit witch I listed below.
748741 - 1967-72 Horn Contact Pin, Spring And Retainer Set Reproduction of the original GM horn contact pin, spring and retainer to fit the turn signal switch cancel cam on various 1964-72 GM models with or without tilt steering wheel. Reproduced to original factory specifications. Each horn contact pin, spring and retainer set is designed to work with OER part #399294 turn signal cancel cam. Fits various models throughout the GM line