[Flathead Fever]

Check to make sure the switch has a good ground. I don't know how its wired, if it has its own separate ground wire or if it clamps to the column and the column provides the ground. The paint could be preventing a good ground or if you insulated it to prevent it from scratching the paint. The turn signal bulbs would work fine because they each have their own grounds. If it is the housing not grounding a quick test would be to jump a wire from the turn signal switch housing to a good ground.

I found a diagram for it and it does look like the hose clamp is providing the ground for the green light.