New switch, the cancelling cam is most likely broken. I think you can still get GM switches from the dealer, at least I did several years ago. Not that expensive and while you have it apart might as well. There are a couple of variations if I remember correctly so you may want to bring it with you to match up.
Many of the autoparts stores carry them in the misc. help yourself parts rack. Quality seemed a bit cheaper than the original but seems to work just fine....
I just had mine off yesterday, it would not cancel left, the bottom spring was broken, they sell them at the local parts store for around a buck each. The switch and springs in your photo look good. It could be the turn signal canceling cam, it rotates around the shaft when you turn the wheel and is also the contact for the horn. It has two bumps on the side that hit the spring as you rotate the wheel and push the switch back to neutral, the bumps could be worn and not moving the springs or maybe weak springs.
There is an exploded pic of the column in the steering section of the 68 service manual in 'The First Gen Site'. Al.
The blinker issue is not even in the top 10 bugs to be fixed. Might be # 11 though. Hope to look at in a couple weeks. Needed to post the question to even know where to start.
now that the blinker is in the top 10 to get fixed I just ordered a cancle cam. I realy want to get my horn working with the sport wheel too.
I still don't know how these parts all go together but It looks like the cancle came is not part of the blinker switch assembly it appears to be a seperate part that I don't have.
I would have to guess that the horn button seen in my pic above rides on the cancle cam and the spring/plunger fit inside of of the cancle cam and up through the hole in the steering wheel to the horn button. I hope the cancle cam fits over the top.
Again I'm only guessing and I hope by getting the horn working I will get the blinker cancle working too.
The cancel cam goes under the steering wheel. The two bumps hit the coiled springs on the turn signal switch to push it back to the neutral position. The horn contact presses against the brass ring on the cancel cam. Wires (not visible in the pic) connect the horn buttons to the brass ring.
The Cancle cam I ordered from Ames came in. It was a factory GM part. Finaly figured it all out. The blinker cancle and the horn now work.
The horn button still had some paint on the end and wasn't making contact so I had to pull the cancle came back out twice. Once it snaps in place its a chore to remove.
I had to pull the spring longer and the black plastic piece was not used.
The instruction with the horn contact kit said to cut out 1/4 inch.