It's my experience that the lock cylinder is locked. Once you get the cylinder out, you can operate the switch with a screwdriver. in fact, after I bought my car I changed the lock cylinder. The switch assembly comes out of the dash with zero tools on my 57.
1) Lean under dash push body of switch towards the back of the car.
2) put your finger tops on the bezel, and rotate it CCW. The bezel can now be pi\ulled away from the dash.
3) withdraw the switch assembly back down from under the dash.
I'd recommend pulling a battery cable. You never know...
In this case, put the key in, and try to turn it like 1/2 way. A paper clip as I recall will push the keeper back, and the cylinder will fall out. Then you should easily be able to operate the switch with a screwdriver. If you can you know the cylinder if the cuplrit. Either a broken spring, or a seized pin.