[6 Grrrs]

The blowup and pics above are of a '67 column, which is different from a '66 column (no hazard switch). nodwyer - it looks like you have a '66.

I had the same trouble with mine. I was not putting it on the column far enough. When you push the housing down, it will rotate clockwise (I think) into position. Also I found that if you put the housing on the column & then put the 3 screws in, it will fit better.

I was fighting with this last summer on my car & finally got it correct. However, that has been a while, so I forget what direction to turn it.

This statement from Jeff makes the most sense in explaining it:

Once the lower pc is screwed to the upper the 2 pcs are now one assy'.
You clearly have that. With the sw wires slipped into the housing you then slide the housing over the shaft tube. You will need to turn it L&R to slip past the tabs and line up the sw lead to the correct location (Flat section on shaft) If you have it correct it should be semi locked within the tabs. Then the 3 screws secure it as stated above by pulling it upward.