I've never pulled apart a '62, but I had the exact same issue with my '55.1 signals. There's a pair of cams that lock the lever in place during a turn, and a really odd-shaped flat spring that maintains pressure on the cams (anchored in the center under the steering shaft and reaches up on either side to the cams). On the back of the steering wheel is a steel ring with about 1/2" tab sticking down into the signal assembly. As you turn the wheel, the tab kicks the cam free and releases the signal switch.

In my case, the cancelling tab was fine, but the spring was broken. I had to fabricate a new one, as I haven't seen any vendors selling just that spring. I must have made the spring too beefy, because now the cams won't hold the switch in place. :rolleyes:

1955 First Series GMC 250 1-Ton Panel
In the Gallery
Mr. Hedgehog - Follow the build
If you can't laugh at yourself, I'll laugh at you.