Hi 62Chevyman,
I also have a 62' chevy, the blinker switch is mounted on top at the base of your steering column.
There is a cable that runs from the turn signal cam, down to the switch at the base of the column.
Also before I replaced my wire harness the flasher needed to be wiggled, or pushed in + out sometimes to get it to work.
Also check your grounds,and the light bulbs.
Does the green light, light up in your dash for either side?
David